PER CURIAM:

Ralph Jason Miller engaged in an ongoing sexual relationship with a minor. He took explicit photographs of her on several occasions, and he asked her to send him explicit photographs of herself. That led to his being charged with, and a jury finding him guilty of, three counts of producing child pornography, in violation of 18 U.S.C. § 2251(a), and of one count of committing those crimes while under obligation to register as a sex offender, in violation of 18 U.S.C. § 2260A. The district court sentenced him to 420 months in prison. Miller appeals his conviction and sentence on the three counts of producing child pornography.

I.

Miller contends that the district court erred by refusing to give one of his proposed jury instructions and by giving an instruction that misstated the law instead. He asked the district court to instruct the jury that the government had to prove that producing child pornography was "one of [his] dominant motives" for causing a minor to engage in sexually explicit conduct. And he objected to the court's instruction, which said that the government had to prove that making child pornography was "a purpose" for doing so. Miller argues on appeal that the district court should have given the pattern jury instruction, which provides that the government must prove that creating a visual depiction was "the purpose" for the defendant's actions. See Eleventh Circuit Pattern Jury Instructions (Criminal Cases) 82 (2010) (emphasis added). According to Miller, the court's use of the indefinite article reduced the government's burden of proof and limited his ability to present an effective defense.

A district court "enjoys broad discretion to formulate jury instructions provided those instructions are correct statements of the law." United States v. Lebowitz, 676 F.3d 1000, 1014 (11th Cir. 2012). We will reverse the rejection of a party's proposed instruction "only if (1) the requested instruction was substantively correct, (2) the court's charge to the jury did not cover the gist of the instruction, and (3) the failure to give the instruction substantially impaired the defendant's ability to present an effective defense." Id. (quotation marks omitted). And we defer to the district court "on questions of phrasing," United States v. Prather, 205 F.3d 1265, 1270 (11th Cir.2000) (quotation marks omitted), reversing "only if we are left with a substantial and eradicable doubt as to whether the jury was properly guided in its deliberations," United States v. Browne, 505 F.3d 1229, 1276 (11th Cir. 2007) (quotation marks omitted).

We have no such doubts here. The district court's instruction was a correct statement of the law: "[W]e have held that dual purposes are sufficient for a conviction" under § 2251(a), and that "we need not concern ourselves with whether the illegal purpose was dominant over other purposes." Lebowitz, 676 F.3d at 1014-15 (quotation marks omitted). And that instruction did not impair Miller's ability to present an effective defense. Miller says that the instruction prevented him from arguing that the photographs were a "mere incident" of his consensual romantic relationship with the minor, but that is not a viable defense to the charge against him. The government was not required to prove that making explicit photographs was Miller's sole or primary purpose for enticing the minor to engage in sexually explicit conduct. It was enough to show that it was "a purpose" for doing so.

II.

Miller next contends that the district court erred by enhancing his sentence under 18 U.S.C. § 2251(e), which imposes a mandatory minimum sentence of 25 years on any defendant convicted of violating § 2251 who has one prior conviction "under the laws of any State relating to aggravated sexual abuse, sexual abuse, abusive sexual contact involving a minor or ward, or sex trafficking of children." 18 U.S.C. § 2251(e). The district court sentenced Miller under that provision because he was convicted of sexual battery in Florida.1 We review de novo the district court's determination that a prior conviction triggers a statutory sentencing enhancement. See United States v. Howard, 742 F.3d 1334, 1341 (11th Cir.2014).

Miller argues that his prior conviction for sexual battery does not qualify under § 2251(e) because it did not require proof that his victim was a minor. See Fla. Stat. § 794.011(5) (1999) (making it a second degree felony to "commit[ ] sexual battery upon a person 12 years of age or older, without that person's consent" and without "us[ing] physical force and violence likely to cause serious personal injury"). According to Miller, only crimes involving minors can trigger an enhanced sentence because the phrase "involving a minor or ward" in § 2251(e) modifies each of the crimes listed before it (i.e., "aggravated sexual abuse," "sexual abuse," and "abusive sexual contact"), instead of only the one crime immediately preceding it ("abusive sexual contact"). We disagree.

In Lockhart v. United States, 577 U.S. ___, 136 S.Ct. 958, 194 L.Ed.2d 48 (2016), the Supreme Court considered closely analogous question in the context of materially indistinguishable statutory language in 18 U.S.C. § 2252(b)(2), which provides that a defendant convicted of possessing child pornography under 18 U.S.C. § 2252(a)(4) is subject to a 10-year mandatory minimum sentence if he has a prior conviction "under the law of any State relating to aggravated sexual abuse, sexual abuse, or abusive sexual conduct involving a minor or ward." Lockhart, 136 S.Ct. at 961 (quoting 18 U.S.C. § 2252(b)(2)). The only difference in the relevant statutory texts is that § 2252(b)(2) refers to "abusive sexual conduct" and § 2251(e) refers to "abusive sexual contact." That distinction obviously is not material.

The Lockhart Court held that the phrase "involving a minor or ward" modified only the crime immediately preceding it in the statute and did not modify the other listed crimes. Id. There is no reasonable justification for treating the same phrase differently where it appears in § 2251(e). We therefore conclude that the 25-year statutory mandatory minimum in § 2251 applies to any defendant with a prior conviction relating to "abusive sexual contact involving a minor or ward," as well as to any defendant with a prior conviction relating to "aggravated sexual abuse" or "sexual abuse," whether or not that conviction involved a minor.2 See id. at 968.

Miller finally contends that, even under that interpretation of § 2251(e), his sexual battery conviction does not trigger the sentencing enhancement because it is not equivalent to a conviction for a crime that would constitute sexual abuse under federal law. That argument ignores the plain text of the statute, which provides that the enhancement applies to any defendant who has a prior state conviction relating to sexual abuse. See 18 U.S.C. § 2251(e). "We have interpreted the phrase `relating to' broadly in the context of child exploitation offenses" like § 2251. United States v. Mathis, 767 F.3d 1264, 1284 (11th Cir. 2014); see also United States v. McGarity, 669 F.3d 1218, 1262 (11th Cir.2012) (explaining that an identical provision in 18 U.S.C. § 2252A "does not simply mandate a sentencing enhancement for individuals convicted of state offenses equivalent to sexual abuse," but "for any state offense that stands in some relation, bears upon, or is associated with" sexual abuse) (citing United States v. Sinerius, 504 F.3d 737, 743 (9th Cir.2007)). Miller's conviction for sexual battery clearly relates to "sexual abuse" as that term is generally understood. See Sinerius, 504 F.3d at 740-43. The district court did not err in enhancing Miller's sentence under § 2251(e) based on that prior conviction.

AFFIRMED.