
510 F.3d 1045 (2007)
Timothy Lee BYRD, Petitioner-Appellant,
v.
Gail LEWIS, Warden, Pleasant Valley State Prison; Edmund G. Brown, Attorney General for the State of California, Respondents-Appellees.
No. 06-15977.
United States Court of Appeals, Ninth Circuit.
Argued and Submitted October 15, 2007.
Filed December 11, 2007.
*1046 Krista Hart (briefed and argued), Sacramento, CA, for the petitioner-appellant.
Edmund G. Brown Jr. (briefed), Dane R. Gillette (briefed), Michael P. Farrell (briefed), Carlos A. Martinez (briefed), and Wanda Hill Rouzan (briefed and argued), Sacramento, CA, for the respondents-appellees.
*1047 Before: J. CLIFFORD WALLACE and JOHNNIE B. RAWLINSON, Circuit Judges, and JANE A. RESTANI,[*] Judge.
Opinion by Judge RAWLINSON; Partial Concurrence and Partial Dissent by Judge WALLACE.
RAWLINSON, Circuit Judge:
Timothy Byrd (Byrd) appeals the district court's denial of his 28 U.S.C. § 2254 habeas corpus petition challenging his jury conviction for unlawfully taking a vehicle under Cal. Vehicle Code § 10851(a). We have jurisdiction under 28 U.S.C. §§ 1291 and 2253. We conclude that the state court's application of harmless error review to the trial court's jury instruction lowering the prosecution's burden of proof was contrary to or an unreasonable application of clearly established Supreme Court precedent. We reverse the district court's denial of Byrd's habeas petition as to that issue. We otherwise affirm the district court's decision.

I. FACTS AND PROCEDURAL HISTORY[1]

A. The Crime
At noon on June 26, 1999, Lorena Coen (Coen) began drinking at her home. Later that afternoon she drove her 1984 Ford Mustang to Lewey G's bar, where she continued to drink until she became intoxicated. Coen attempted to leave Lewey G's but realized that she was too intoxicated to drive. Instead, Coen decided to park her car one-half block away, across the street from the house of two acquaintances.
Eugean Allen (Allen), a man Coen had known for years, who is also Byrd's cousin, saw Coen and invited her to a party. Coen continued to drink at the party. During the course of the party, Coen drove between the party and Lewey G's with other people in the car, possibly including Byrd. Coen subsequently called her boyfriend to take her home, but she could not find her keys. She locked her car manually, intending to return for it the following day. However, when Coen's boyfriend returned for the car, he discovered that it was not where Coen had parked it. Coen then reported her car stolen.
A few days later, two California Highway Patrol Officers stopped Byrd. Initially, Byrd falsely identified himself. Upon investigation, the officers discovered that the car Byrd was driving belonged to Coen. A search of the car revealed that the radio had been removed and that the headliner was torn. After being given his Miranda[2] warnings, Byrd explained that a girl named "Lorie" loaned him the car.
After retrieving her car, Coen confirmed that the radio had been ripped out and the headliner was gone. She also noted that things she had kept in her carsome clothes, her purse and her son's toys  were missing. Additionally, the car would no longer move in reverse. By the time Coen got home, the car would not move forward either.

B. The Trial
Byrd was charged with, among other things, unlawfully driving or taking a vehicle *1048 in violation of Cal. Veh.Code § 10851(a). At trial, Coen testified that she did not recall whether she gave her keys to Byrd. However, she explained that she did not believe that she lent Byrd her car for several days because she had never done so before, and needed her car to drive to work.[3] Sandra Coen, Coen's sister-in-law, testified that Coen usually did not lend her car to anyone. Allen testified for the defense, recounting that Coen told Byrd that Byrd could have the keys to her car as she no longer wanted it.
The jury convicted Byrd, and he was sentenced to a prison term of twenty-five years to life.

C. Post-Trial Proceedings
The California Court of Appeal affirmed Byrd's conviction. The California Supreme Court summarily denied Byrd's petition for review, after which Byrd filed a federal petition for a writ of habeas corpus. Byrd's case was referred to a Magistrate Judge who recommended denying Byrd's habeas petition. The Magistrate Judge's Findings and Recommendations were fully adopted by the district court. The district court subsequently granted a certificate of appealability on the following issues raised by Byrd on appeal: (1) "[the trial court's] failure to sua sponte instruct the jury on mistake of fact," and (2) "the trial court's jury instruction that the jury could find specific intent for vehicle theft based on [Byrd's] retention of the car beyond the scope of consent[.]"

II. STANDARD OF REVIEW
We review de novo the district court's decision to deny Byrd's habeas petition. Nguyen v. Garcia, 477 F.3d 716, 721 (9th Cir.2007). Because Byrd filed his habeas petition after April 24, 1996, his appeal is governed by the Antiterrorism and Effective Death Penalty Act (AEDPA). See Gill v. Ayers, 342 F.3d 911, 917 (9th Cir.2003). Under AEDPA, Byrd's petition can be granted only if the state court determination resolving his claims "was contrary to, or involved an unreasonable application of, clearly established Federal law ..." or "was based on an unreasonable determination of the facts ..." 28 U.S.C. § 2254(d). "A state court's decision is contrary to clearly established federal law if it (1) applies a rule that contradicts the governing law set forth in Supreme Court cases, or (2) confronts a set of facts materially indistinguishable from a Supreme Court decision and nevertheless arrives at a different result." Gibson v. Ortiz, 387 F.3d 812, 814 (9th Cir.2004) (citations omitted). "A state court's decision is an unreasonable application of clearly established federal law if the state court identifies the correct governing legal principles from Supreme Court decisions but unreasonably applies that principle to the facts of the prisoner's case." Id. (citation, alteration and internal quotation marks omitted).

III. DISCUSSION[4]

A. Mistake-of-Fact Instruction
Byrd contends that because there was evidence demonstrating that Coen gave him permission to drive her car, his due process rights were violated by the trial court's failure to sua sponte instruct the jury regarding mistake-of-fact. Accordingly, Byrd argues, the California Court of *1049 Appeal's ruling that "substantial evidence supported the [mistake-of-fact] instruction, but ... the trial court's error in failing to give it was not prejudicial[,]" Byrd, 2001 WL 1480516, at * 3, was contrary to clearly established Supreme Court precedent. We disagree.
"Failure to instruct on the defense theory of the case is reversible error if the theory is legally sound and evidence in the case makes it applicable." Beardslee v. Woodford, 358 F.3d 560, 577 (9th Cir.2004) (citation omitted).[5] However, to obtain relief, "[Byrd] must show that the alleged instructional error had substantial and injurious effect or influence in determining the jury's verdict." Clark v. Brown, 450 F.3d 898, 905 (9th Cir.2006), as amended (citations and internal quotation marks omitted); see also Beardslee, 358 F.3d at 578. A "substantial and injurious effect" means a "reasonable probability" that the jury would have arrived at a different verdict had the instruction been given. Clark, 450 F.3d at 916. To decide whether Byrd was prejudiced, we consider: (1) the weight of evidence that contradicts the defense; and (2) whether the defense could have completely absolved the defendant of the charge. See Beardslee, 358 F.3d at 578. "The burden on [Byrd] is especially heavy where ... the alleged error involves the failure to give an instruction." Clark, 450 F.3d at 904 (citation and internal quotation marks omitted).
Notwithstanding Byrd's innocuous explanations for the facts that he: (1) kept Coen's car for five days; (2) did not attempt to return Coen's car; and (3) removed personal effects from Coen's car, the other evidence overwhelmingly demonstrates that no reasonable juror would have concluded that Byrd actually believed that Coen loaned Byrd her car temporarily or gave it to him. As the California Court of Appeal reasoned:
[Byrd's] claim that Coen lent him the car is convincingly belied by the following facts: ... [T]he car radio [was removed from the car] and ... the interior of the car had been damaged.... It is even less likely[ ] that the jury would have thought[Byrd] believed Coen gave him the car permanently. This would have required the jury to conclude that [petitioner] believed a thoroughly intoxicated woman, whom he barely knew, would intentionally give him the gift of a 1984 Ford Mustang containing her personal items including her purse.
Byrd, 2001 WL 1480516, at * 6; see also Beardslee, 358 F.3d at 578 (concluding that failure to provide a correct mistake-of-fact jury instruction was not prejudicial where "a significant amount of evidence countered the mistake-of-fact theory."). Accordingly, the California Court of Appeal's ruling regarding failure of the trial court to sua sponte instruct the jury on mistake-of-fact was not contrary to or an unreasonable application of clearly established Federal law. We affirm the district court's denial of habeas relief as to this claim.

B. Scope-of-Consent Instruction
Byrd also challenges the trial court's scope-of-consent instruction, which provided:
The failure to return a vehicle that was obtained by consent in a timely manner does not by itself establish a violation of section 10851.... You should determine from the circumstances whether the continued use of a vehicle both as to the length of time and the manner clearly and substantially exceeded the scope of the consent given. If it does not clearly *1050 and substantially exceed the scope of the consent given, then the required criminal intent would not be clearly established.

Byrd, 2001 WL 1480516, at * 7 (emphasis added).[6] According to Byrd, this instruction diluted the prosecution's burden of proof, thereby violating his right to due process. The California Court of Appeal agreed, reasoning that because a "clearly established" standard was applied to define the requisite criminal intent, "it is reasonably likely the jury did not find that [Byrd] exceeded Coen's scope of consent beyond a reasonable doubt ..." Byrd, 2001 WL 1480516, at * 10. However, the California Court of Appeal concluded that harmless error analysis was applicable because the instruction was "an error that acknowledges the element, but subjects the element to a lesser burden of proof." Id. at * 11.
"Any jury instruction that reduces the level of proof necessary for the Government to carry its burden is plainly inconsistent with the constitutionally rooted presumption of innocence." Gibson, 387 F.3d at 820 (citation, alterations, and internal quotation marks omitted). In this case, the scope-of-consent instruction was defective because it impermissibly lowered the state's burden of proof on whether Byrd took Coen's car without her consent. Indeed, as in Gibson and as expressly noted by the California Court of Appeal, the scope-of-consent instruction permitted the jury to "conclude[ ] [that Byrd's] `criminal intent' to keep the car beyond [Coen's] permission need only be `clearly established' ... if the jury decided [Byrd] `clearly and substantially exceeded' the scope of Coen's consent." Byrd, 2001 WL 1480516, at * 10; cf. Gibson, 387 F.3d at 822 (concluding that jury instructions allowing the jury to conclude based on a preponderance of the evidence that petitioner committed uncharged offenses, and infer based on the uncharged offenses that he had committed the charged offense impermissibly lowered the government's burden of proof). Ultimately, the California Court of Appeal held that "it is reasonably likely the jury did not find that [Byrd] exceeded Coen's scope of consent beyond a reasonable doubt, thus, violating [Byrd's] right to due process of law." Byrd, 2001 WL 1480516, at * 10.
When considering a claim of instructional error, "the proper inquiry is not whether the instruction `could have' been applied in an unconstitutional matter, but whether there is a reasonable likelihood that the jury did so apply it." Victor v. Nebraska, 511 U.S. 1, 6, 114 S.Ct. 1239, 127 L.Ed.2d 583 (1994) (emphasis in the original).[7] Indeed, "[the] challenged instruction must be considered in light of the full set of jury instructions and the trial record as a whole." Gibson, 387 F.3d at 821 (citation omitted); see also Victor, 511 U.S. at 5, 114 S.Ct. 1239.
Several general jury instructions were read that described the beyond-a-reasonable doubt burden of proof. However, as the California Court of Appeal reported, during deliberations, "[t]he jury asked, `On second element permission, if the permission was initially given, when does permission run out[?]'" (internal quotation marks *1051 and alteration omitted). Byrd, 2001 WL 1480516, at * 7. "In response, the court instructed the jury in writing to see `instruction No. 23,' which was the scope of consent instruction." Id. As discussed, this instruction does not reference the correct beyond-a-reasonable-doubt burden of proof as to scope-of-consent. Moreover, the fact that during deliberations the trial judge directed the jury to this instruction, without referencing any of the beyond-a-reasonable doubt instructions, increased the likelihood that the jury applied the lowered burden of proof reflected in the instruction. See United States v. Miller, 546 F.2d 320, 324 n. 3 (9th Cir.1976) (explaining that rereading particular instructions may "over-emphasize" them to the jury). Thus, the state court's determination that the scope-of-consent instruction impermissibly lowered the prosecution's burden of proof on an element of the offense was not contrary to or an unreasonable application of Supreme Court law regarding proof of guilt beyond a reasonable doubt.
We reach a different conclusion regarding the California Court of Appeal's reasoning that "an error that acknowledges [an] element, but subjects the element to a lesser burden of proof" constitutes trial error. Byrd, 2001 WL 1480516, at * 11; cf. Gibson, 387 F.3d at 824 (holding that an instruction permitting the jury to find the defendant guilty by a preponderance of the evidence "constituted structural error within the meaning of Sullivan [v. Louisiana, 508 U.S. 275, 113 S.Ct. 2078, 124 L.Ed.2d 182 (1993)]") (citation omitted). In Sullivan, the Supreme Court held that where a jury instruction "consists of a misdescription of the burden of proof, [it] vitiates all the jury's findings." Sullivan, 508 U.S. at 281, 113 S.Ct. 2078 (emphasis in the original). Indeed, according to Sullivan, "[d]enial of the right to a jury verdict of guilt beyond a reasonable doubt is certainly [structural error]." Id. Once the California Court of Appeal determined that the scope-of-consent instruction impermissibly lowered the government's burden of proof as to the consent element of the crime, application of harmless error review was no longer an option. See id. Accordingly, the California Court of Appeal's court's holding that the erroneous scope-of-consent instruction was harmless was contrary to or an unreasonable application of clearly established federal law. See id. We reverse the district court's denial of habeas relief on this claim.

IV. CONCLUSION
Because the trial court's failure to sua sponte give a mistake-of-fact instruction did not prejudice Byrd, the state court's denial of this claim was not contrary to or an unreasonable application of Supreme Court precedent. However, the state court's harmless error review of the jury instruction lowering the prosecution's burden of proof was contrary to or an unreasonable application of Supreme Court precedent. Accordingly we AFFIRM the district court's denial of relief on Byrd's mistake-of-fact instruction claim and REVERSE the district court's denial of relief on Byrd's burden-of-proof instruction claim. We REMAND with instructions that the district court grant the writ of habeas corpus unless the State grants Byrd a new trial within a reasonable period of time.
AFFIRMED in part, REVERSED in part and REMANDED. Each party is to bear its costs on appeal.
WALLACE, Circuit Judge, concurring and dissenting:
Although I agree with the majority on the mistake of fact issue, I respectfully dissent from the remainder of the majority's decision on two grounds. First, I do *1052 not believe it was reasonably likely that the jury applied the scope-of-consent instruction in an unconstitutional manner, and I would hold that the California Court of Appeal unreasonably applied Supreme Court precedent when it reached the opposite conclusion. Second, even if the court were correct on the first issue, I do not believe the California Court of Appeal unreasonably applied Supreme Court law when it reviewed the disputed instruction for harmless error.

I.
The Supreme Court has established that "in reviewing an ambiguous instruction ... we inquire whether there is a reasonable likelihood that the jury has applied the challenged instruction in a way that violates the Constitution." Estelle v. McGuire, 502 U.S. 62, 72, 112 S.Ct. 475, 116 L.Ed.2d 385 (1991) (internal quotation marks omitted). Indeed, "the proper inquiry is not whether the instruction `could have' been applied in an unconstitutional manner, but whether there is a reasonable likelihood that the jury did so apply." Victor v. Nebraska, 511 U.S. 1, 6, 114 S.Ct. 1239, 127 L.Ed.2d 583 (1994).
The jury instruction at issue here was ambiguous. The California Court of Appeal was therefore required, under Estelle, to determine whether it was reasonably likely that the jury applied the instruction in an unconstitutional manner. The court held that it was, based on a question posed by the jury during deliberations. The jury asked: "On second element permission, if the permission was initially given, when does permission run out[?]" The trial court responded by directing the jury to the disputed scope-of-consent instruction.
Prior to deliberations, the court provided the jury with three clearly-enumerated elements of the charged crime: (1) taking or driving of a vehicle, (2) without consent, and (3) with specific intent to deprive the owner of title or possession. Thus, when the jury inquired about the "second element" they were referring specifically to the element of consent.
To understand why it was unreasonable for the California Court of Appeal to conclude that the jury unconstitutionally applied the instruction, it is important to review the Court of Appeal's somewhat convoluted textual interpretation of the instruction. The court analyzed the last two sentences of the instruction independently. With respect to the first, the court held that it imposed a higher burden of proof on the consent element, and therefore the "instructional shortcoming was to defendant's benefit and it is not error as to him." People v. Byrd, No. C034582, 2001 WL 1480516, at *9 (Cal.Ct.App. Nov.21, 2001), as modified on denial of reh'g (Dec. 20, 2001). Therefore, because the jury asked specifically about the "second element" of consent, under the Court of Appeal's own analysis, the instruction the jury received was free from constitutional error.
It was only with respect to the final sentence of the instruction that the California Court of Appeal found constitutional error. That sentence involved the interplay between the elements of consent and intent: "If [the use of the vehicle] does not clearly and substantially exceed the scope of the consent given, then the required criminal intent would not be clearly established." The court held that, once the word "not" was removed from the sentence, the instruction impermissibly allowed the jury to find intent based solely on a finding of consent. Furthermore, the court held that the jury might make such a finding at a burden lower than beyond a reasonable doubt. All of these concerns, however, dealt with the element of intent. Had the jury requested clarification on the "third element," and been directed to the *1053 disputed instruction, it would have been reasonable for the California Court of Appeal to conclude the jury had applied it in an unconstitutional manner. However, because the jury only inquired about consent, then under the logic of the court's own interpretation, no constitutional concerns were directly implicated.
The California Court of Appeal offers only one hypothetical situation that could potentially explain how the jury, concerned only with the "second element," would have nonetheless applied an unconstitutionally lowered burden of proof. The court reasoned:
Upon consideration of [the consent element] the jury may have decided that Coen initially gave defendant permission to take her car for the evening, at which point it would have turned to the court's instruction on the effect of Coen's consent ... on the second element of the offense.[1] So doing, it may have concluded defendant's "criminal intent" to keep the car beyond the owner's permission need only be "clearly established" and that it could be "clearly established," if the jury decided defendant "clearly and substantially exceeded" the scope of Coen's consent. Thus, we conclude it is reasonably likely the jury did not find that defendant exceeded Coen's scope of consent beyond a reasonable doubt, thus, violating defendant's right to due process of law.
Byrd, 2001 WL 1480516, at * 10. Under this reasoning, to the extent I can understand it, the jury would have been required, initially, to read out the word "not" from the instructions. It would have then needed to consider how the element of consent affected the element of intent. Finally, the jury would have been required to import a lower standard of proof from the intent element when making its consent determination. I do not believe it was reasonably likely that any jury would engage in such tortured analysis. That should have ended this case.

II.
But, the majority holds that the California Court of Appeal unreasonably applied established Supreme Court law when it reviewed the disputed jury instruction for harmless error. As argued above, I do not believe it is reasonably likely that the jury actually applied the instructions in an unconstitutional manner, so I would affirm without reaching the issue of structural error. However, even assuming the jury actually applied the instruction unconstitutionally, under the facts of this case, I do not believe Supreme Court precedent compelled the California Court of Appeal to conclude there was structural error. Therefore, I depart from the majority's analysis.
The majority points to Sullivan v. Louisiana, 508 U.S. 275, 113 S.Ct. 2078, 124 L.Ed.2d 182 (1993), for the proposition that any time a jury instruction "consists of a misdescription of the burden of proof, [it] vitiates all the jury's findings." Id. at 281, 113 S.Ct. 2078. I do not believe Sullivan can be stretched to such a broad proposition. In Sullivan, the trial court gave the jury a single definition of "reasonable doubt." Id. at 277, 113 S.Ct. 2078. That definition was unconstitutional, and it infected all of the jury's findings. The Court only found that the instruction "vitiates all the jury's findings," because the instruction applied to all of the jury's findings. Id. at 281, 113 S.Ct. 2078. Not surprisingly, the Supreme Court held that there was nothing "upon which harmless-error *1054 scrutiny can operate." Id. at 280, 113 S.Ct. 2078.
The facts of this case are far different. On several occasions, the trial court instructed the jury that each factual finding and element of the crime had to be supported by proof beyond a reasonable doubt. Under the California Court of Appeal's analysis, it was only with respect to the single issue of consent that the jury could  through its tortured reading of the instruction  potentially have determined that a lower burden was appropriate. Unlike Sullivan, in which all of the jury's findings were infected, the error in this case was discrete. It was limited to a single hypothetical interpretation of a single sentence with respect to a single element of the crime. Therefore, I do not believe it was an unreasonable application of Supreme Court precedent for the court to analogize this case more closely to Pope v. Illinois, 481 U.S. 497, 107 S.Ct. 1918, 95 L.Ed.2d 439 (1987), in which the Court applied harmless error review to jury instructions that misstated a single element of the offense.
Finally, although the facts of our decision in Gibson v. Ortiz, 387 F.3d 812 (9th Cir.2004) are more analogous than those of Sullivan, "the only definitive source of clearly established federal law under AEDPA is the holdings ... of the Supreme Court as of the time of the state court decision." Clark v. Murphy, 331 F.3d 1062, 1069 (9th Cir.2003). While circuit law, like Gibson, may provide "persuasive authority" for purposes of determining whether a state court decision is an unreasonable application of Supreme Court precedent, "only the Supreme Court's holdings are binding on the state courts and only those holdings need be reasonably applied."
Id. Because the facts of this case are materially distinguishable from those in Sullivan, I conclude it was not an unreasonable application of clearly established federal law for the court to apply harmless error review.
NOTES
[*]  The Honorable Jane A. Restani, Chief Judge, United States Court of International Trade, sitting by designation.
[1]  The facts are taken from the opinion of the California Court of Appeal. See People v. Byrd, No. C034582, 2001 WL 1480516, at *1-3 (Cal.Ct.App. Nov.21, 2001), as modified on denial of reh'g (Dec. 20, 2001). The California Court of Appeal's findings of fact are presumed correct "unless [Byrd] can prove otherwise by clear and convincing evidence." Sanders v. Lamarque, 357 F.3d 943, 948 (9th Cir.2004) (citations omitted).
[2]  Miranda v. Arizona, 384 U.S. 436, 86 S.Ct. 1602, 16 L.Ed.2d 694 (1966).
[3]  "While her car was missing, [Coen] temporarily lost her job." Byrd, 2001 WL 1480516, at * 2.
[4]  In considering potential state court error, we look to the "last reasoned decision of the state court as the basis of the state court's judgment." Franklin v. Johnson, 290 F.3d 1223, 1233 n. 3 (9th Cir.2002) (citation omitted). The California Court of Appeal's decision affirming Byrd's conviction represents the last reasoned state court decision.
[5]  Although circuit caselaw is not governing law under AEDPA, this Court may look to circuit precedent in determining what law is clearly established. See Duhaime v. Ducharme, 200 F.3d 597, 600-01 (9th Cir.2000), as amended.
[6]  The scope-of-consent instruction was given both orally and in writing. The oral scope-of-consent instruction differed from the written instruction, adding the word "clearly" to modify the criminal intent requirement. However, because Byrd's contention is that the instruction diluted the beyond-a-reasonable doubt standard, the difference in the oral and written instructions is immaterial.
[7]  A "reasonable likelihood" is lower than the "more likely than not" standard. See Boyde v. California, 494 U.S. 370, 380, 110 S.Ct. 1190, 108 L.Ed.2d 316 (1990).
[1]  Although the court uses the term "second element" it appears to be referring to the third element of intent.
