
93 P.3d 206 (2004)
122 Wash.App. 294
STATE of Washington, Respondent,
v.
William A. SMITH, Appellant.
No. 29805-8-II.
Court of Appeals of Washington, Division 2.
July 7, 2004.
*207 Thomas Edward Doyle, Attorney at Law, Hansville, WA, Patricia Anne Pethick, Attorney at Law, Tacoma, WA, for Appellant.
Monty Dale Cobb, Mason County Prosecutors Office, Shelton, WA, for Respondent.
QUINN-BRINTNALL, C.J.
A jury convicted William Aaron Smith of four counts of third degree rape of a child. Smith appeals, claiming that the trial court erred by instructing the jury that the victim must be between 12 and 16 years of age when the statute requires that the victim be between 14 and 16 years of age. Because the age of the victim is a function of the proper penalty and not an essential element of the proscribed offense of having sexual intercourse with a minor, we affirm.

FACTS
The victim, K.C., was born on June 5, 1987. Smith was a friend of K.C.'s mother. Smith met K.C. in June 2000, soon after K.C.'s 13th birthday.
In May 2002, K.C. told police that she and Smith engaged in sexual intercourse on four separate occasions. K.C. said that she and Smith first had sexual intercourse in July 2001, and the last time in May 2002. K.C. was 14 years old throughout this time frame.
The State charged Smith with four counts of third degree rape of a child, which is the proper charge when the victim is between 14 and 16 years of age at the time of the alleged sexual intercourse.
But during trial, K.C. testified that the first two times she and Smith had sexual intercourse was actually in June 2000, when she was 13 years old. K.C. testified that she knew the first two incidents occurred in June 2000, because they occurred around the time she attended an event called "OzzFest," soon after her 13th birthday. K.C. testified that the only time she and Smith had sexual intercourse in 2001 was the third time, which occurred around September. Thus the evidence established that two of the incidents allegedly occurred when K.C. was 13 and two when she was 14 years old.
*208 The State amended Counts II and III to reflect K.C.'s age at the times indicated in her testimony but did not amend the information to charge second degree rape of a child. The amended information included the definition of third degree rape of a child, including the provision that the child was between 14 and 16 years of age. But the parties agreed to define third degree rape of a child to the jury as:
[s]exual intercourse with another person who is at least twelve years old but less than sixteen years and who is not married to the perpetrator and the perpetrator is at least forty-eight months older than the victim.
Clerk's Papers (CP) at 37 (emphasis added).
Because K.C. was actually 13 years old when two of the alleged events occurred, the court also accepted the State's to-convict instructions that had been modified to reflect the agreed definition. These to-convict instructions required that the jury find the victim was between 12 and 16 years old at the time of sexual intercourse. Both parties, as well as the trial court, were aware that the instruction was a "hybrid" of the second and third degree rape of a child definitions. And neither party disputed that K.C. was 13 at the time the first two incidents were alleged to have occurred. The defense did not object to these instructions.
The court gave the agreed modified definitional and unchallenged to-convict instructions to the jury, which returned a guilty verdict on all four counts.

ANALYSIS
On appeal, Smith contends for the first time that the trial court's "to-convict" instructions were constitutionally defective and that they misstated an element of the crime of third degree rape of a child. RCW 9A.44.079(1) provides:
A person is guilty of rape of a child in the third degree when the person has sexual intercourse with another who is at least fourteen years old but less than sixteen years old and not married to the perpetrator and the perpetrator is at least forty-eight months older than the victim.
(Emphasis added.)
But, as amended, the definitional instruction and the unchallenged elements instructions did not relieve the State of its burden of proving all essential elements of the crime of rape of a child. K.C.'s testimony, if found credible by the jury, established that Smith committed the crime of rape of a child, and that, in at least two instances, he committed second degree rape of a child rather than third degree rape of a child. The fact that the victim was younger than the age range in the third degree rape of a child statute does not mean that the defendant did not commit the proscribed act of having sexual intercourse with a child. See State v. Dodd, 53 Wash.App. 178, 181, 765 P.2d 1337 (1989).
In Dodd, a jury convicted the defendant of third degree statutory rape even though the victim was actually 13 years old. 53 Wash.App. at 179-80, 765 P.2d 1337. The defendant argued that he reasonably believed that the victim was between 14 and 16 years of age. Dodd, 53 Wash.App. at 179-80, 765 P.2d 1337. The Dodd court noted that the act was still an illegal act whether the victim was 13 or 14 and that defendant's reasonable mistake as to the victim's age was not a defense, so long as the defendant believed the victim was less than 16 at the time the crime was committed. 53 Wash.App. at 181, 765 P.2d 1337.[1] We agree with Dodd that "third degree statutory rape is a crime of inferior degree to second degree statutory rape, as each proscribes but one offense, that of sexual intercourse with one too immature to rationally or legally consent to the act." 53 Wash.App. at 181, 765 P.2d 1337. The evidence established that K.C. was 13 years old at the time of the June 2000 acts and that Smith committed the proscribed offense, that is, sexual intercourse with a minor under 16 years of age.
*209 Here, the State charged Smith with a lesser offense than that proved by the evidence. While it may well have been precluded from amending the information and have been bound to continue with the lesser charge filed,[2] it does not follow that proof of the greater charge requires acquittal of the lesser. To the contrary, proof of a greater charge necessarily establishes proof of all lesser included offenses. Likewise, a defendant may be convicted of an offense that is an inferior degree to the one charged, RCW 10.61.003, provided that the statutes, as here, proscribe but one offense. Dodd, 53 Wash.App. at 181, 765 P.2d 1337 (citing State v. Foster, 91 Wash.2d 466, 471-72, 589 P.2d 789 (1979)).
Although we have addressed the merits of Smith's appeal, we also note that Smith is technically precluded from challenging this instruction under the invited error doctrine. Under this doctrine, the jury instructions not objected to became the law of the case. State v. Hickman, 135 Wash.2d 97, 102, 954 P.2d 900 (1998) (citing State v. Hames, 74 Wash.2d 721, 725, 446 P.2d 344 (1968)). Defense counsel participated in crafting the instructions he now seeks to challenge. Error, if any, was invited and the instructions became the law of the case. State v. Studd, 137 Wash.2d 533, 546, 973 P.2d 1049 (1999) (defendant may not set up an error at trial and complain about it on appeal). Thus, Smith may not challenge the instruction.
Smith argues that he is not barred from challenging the instruction on appeal because his counsel was constitutionally ineffective either for failing to object or for acquiescing in the giving of these jury instructions. To establish ineffective assistance of counsel, the defendant must demonstrate (1) deficient performance that caused (2) prejudice to the defense. State v. Tilton, 149 Wash.2d 775, 783-84, 72 P.3d 735 (2003). To overcome the strong presumption in favor of effective counsel, the defendant must prove that there is no legitimate strategic or tactical reason for the deficient performance. State v. McFarland, 127 Wash.2d 322, 335-36, 899 P.2d 1251 (1995). Prejudice occurs if, "there is a reasonable probability that, but for counsel's errors, the result of the trial would have been different." State v. Bennett, 87 Wash.App. 73, 82, 940 P.2d 299 (1997), aff'd, 137 Wash.2d 533, 973 P.2d 1049 (1999). To demonstrate prejudice here, Smith must show that the trial court would have granted a defense motion to dismiss the two charges after K.C. testified that she was only 13 years old during two of the incidents. But as demonstrated above, the evidence established that Smith had sexual intercourse with a minor under 16 years of age and Smith cannot show that the trial court would have granted a motion to dismiss. Counsel's representation was not deficient and did not prejudice Smith.
We affirm.
We concur: MORGAN and HUNT, JJ.
NOTES
[1]  At the time Dodd was decided, the name of this crime was statutory rape, but the victim age elements are identical to the current offense of rape of a child. Compare RCW 9A.44.079 and former RCW 9A.44.090 (1979). The new statute added the requirement that the defendant must be at least 48 months older than the victim, a matter not disputed here.
[2]  See State v. Pelkey, 109 Wash.2d 484, 491, 745 P.2d 854 (1987) (State precluded from amending information to a higher degree offense after resting its case).
