
125 Wis.2d 293 (1985)
371 N.W.2d 411
STATE of Wisconsin, Plaintiff-Respondent,
v.
Wayne J. DANFORTH, Defendant-Appellant.[]
No. 85-210-CR.
Court of Appeals of Wisconsin.
Submitted on briefs April 29, 1985.
Decided June 18, 1985.
*294 For the appellant there were briefs by Leonard D. Kachinsky, of Neenah.
For the respondent there was a brief by Bronson C. La Follette, attorney general, and Kirbie Knutson, assistant attorney general.
Before Cane, P.J., Dean and LaRocque, JJ.
LAROCQUE, J.
Wayne Danforth appeals a judgment convicting him of cruelly maltreating a child, contrary to sec. 940.201,[1] Stats. He claims that the trial court erred by admitting evidence that he struck the victim on two prior occasions and by refusing to instruct the jury on battery, sec. 940.19(1), Stats., as a lesser included offense. Because the trial court's error in admitting the evidence was harmless and because battery is not a lesser included offense of child abuse, we affirm the judgment.
The three-year-old victim suffered abdominal injuries from a blow to the stomach. Over Danforth's objection, the trial court admitted Danforth's admission that he struck the victim on the buttocks "quite hard" earlier that day and that several months earlier he had bloodied the child's nose and blackened his eyes. At trial, hospital *295 personnel described the color and appearance of the bruises on the victim's buttocks and estimated how recently the victim sustained the bruises.
The trial court admitted this evidence of other wrongs under sec. 904.04(2), Stats., as relevant to the issue of Danforth's intent. The evidence, however, is admissible only if it is relevant to an issue in the case. State v. Pharr, 115 Wis. 2d 334, 344, 340 N.W.2d 498, 502 (1983). The court followed the pattern instruction, Wis JI Criminal 1221 (1982), and instructed the jury that before they could convict Danforth, they had to find that he intentionally subjected the child to cruel maltreatment.
Intent is an element of a crime only if it is required by statute. State v. Swanson, 92 Wis. 2d 310, 320, 284 N.W.2d 655, 660 (1979). The term "intentionally," the phrases "with intent to" and "with intent that," and forms of the verbs "know" or "believe" show that criminal intent is an element of a crime in chs. 939 to 948, Stats. Section 939.23(1), Stats. None of these terms are used in the child abuse statute. The word "cruel" in sec. 940.201 does not establish malice as an element of child abuse. State v. Killory, 73 Wis. 2d 400, 413, 243 N.W.2d 475, 483 (1976); see also State v. Stanfield, 105 Wis. 2d 553, 559, 314 N.W.2d 339, 342 (1982) (intent is not an element of sec. 948.02, Stats., which prohibits an individual from "treat[ing] any animal . . . in a cruel manner"). Because none of the sec. 939.23(1) terms are used in the child abuse statute, we conclude that specific intent is not an element of the crime. Section 940.201 requires only the intent to do the act that causes the injury; the resulting injury itself need not be intended.
Because specific intent is not an element of child abuse, the trial court erred in admitting evidence that Danforth struck the child on two earlier occasions.[2] To determine *296 whether this error is harmless, we assess whether the result might probably have been more favorable to Danforth had the error not occurred, see State v. Sonnenberg, 117 Wis. 2d 159, 179, 344 N.W.2d 95, 105 (1984), assuming the state had properly prosecuted him only under a general intent theory.
We conclude that there was sufficient evidence independent of the evidence erroneously admitted to have permitted the jury to conclude that Danforth was guilty beyond a reasonable doubt. Three days after the incident, Danforth told police that the child fell on a toy and vomited sour milk he was accidentally given with his breakfast cereal. Danforth gave the child stomach thrusts to aid him in expelling the sour milk. Eleven days after the incident, Danforth gave another statement to the police. He told them that on the morning of the incident, he had a hangover, the child urinated on the floor, and he struck the child twice on the buttocks. The child vomited, and Danforth hit the child in the stomach. Danforth again told the police about the stomach thrusts he gave the child. Besides the inconsistent stories, Danforth wrote an incriminating letter to the trial judge that the prosecutor read to the jury. Also, a nurse testified that the child told her that "Daddy hit me." In view of this over-whelming evidence, we cannot say that on a retrial with the proper jury instruction, the result might probably be more favorable to Danforth. We therefore conclude that the error was harmless beyond a reasonable doubt.
*297 [3]
Danforth also argues that the trial court erred by refusing to instruct the jury on battery as a lesser included offense of child abuse. A trial court has broad discretion in instructing the jury. State v. Ivy, 115 Wis. 2d 645, 650, 341 N.W.2d 408, 411 (Ct. App. 1983), rev'd on other grounds, 119 Wis. 2d 591, 350 N.W.2d 622 (1984). The instructions, however, must fairly inform the jury of the law that applies to the case. State v. Turner, 114 Wis. 2d 544, 551, 339 N.W.2d 134, 138 (Ct. App. 1983).
[4]
The trial court properly refused Danforth's request for a battery instruction because the law of battery does not apply to this case. To determine whether one crime is a lesser included offense of another crime, see sec. 939.66 (1), Stats., we examine the statutory definitions of the two crimes. State v. Verhasselt, 83 Wis. 2d 647, 664, 266 N.W.2d 342, 350 (1978). Battery requires proof of facts different from those required to prove the crime charged, child abuse. The elements of battery are (1) bodily harm to another person (2) by an act intended to cause bodily harm (3) without the consent of the person harmed. Section 940.19(1), Stats. The elements of child abuse are (1) torture or cruel maltreatment (2) of a child under sixteen years of age. Section 940.201, Stats. None of the elements of battery are elements of child abuse. Battery is therefore not a lesser included offense of child abuse.
By the Court.Judgment affirmed.
NOTES
[]  Petition to review granted.
[1]  Section 940.201, Stats., provides:

Whoever tortures a child or subjects a child to cruel maltreatment, including, but not limited to, severe bruising, lacerations, fractured bones, burns, internal injuries or any injury constituting great bodily harm under s. 939.22(14), is guilty of a Class E felony. In this section, "child" means a person under 16 years of age.
[2]  The state, the defense, and the trial court all assumed that sec. 940.201, Stats., requires proof of specific intent. See Wis JI Criminal 1221 (1982). Under such a theory, the admission of evidence of other wrongs would be proper if used to prove specific intent, provided the court weighed the relevance against any prejudice to the defendant. Because Danforth consistently protested the relevance of the other wrongs evidence, and because of the importance of resolving the question whether the state must prove intent in sec. 940.201 prosections, we do not treat Danforth's failure to object to the specific intent jury instruction as a waiver.
