On Tuesday, presidential front-runners Hillary Clinton and Donald Trump built on their leads for their respective parties’ nominations. In the process, they offered a preview of what could be a major—and particularly nasty—general-election theme.

On Monday, Clinton appeared at a town-hall event where she promised if elected, that half of her cabinet would be women. (Canadian Prime Minister Justin Trudeau did that last year.) Tuesday started off with Donald Trump on Fox and Friends, where he replied. “I call her 'Crooked Hillary' because she’s crooked, and you know the only thing she’s got is the woman card,” he said. “That’s all she’s got, and it is pandering. It’s a weak card in her hands. In another person’s hands it could be a powerful card. I’d love to see a woman president, but she’s the wrong person.”

When Clinton went on stage Tuesday night in Philadelphia, she was more than happy to reply to that. “The other day, Mr. Trump accused me, of playing the, quote, ‘woman card,’” she said. “Well, if fighting for women's health care and paid family leave and equal pay is playing the woman card, then deal me in.”

A little later in the evening, Trump spoke at his eponymous tower to celebrate his win. He left his most controversial comments for the end.

“Frankly, if Hillary Clinton were a man, I don't think she'd get 5 percent of the vote. The only thing she's got going is the women's card,” he said. “And the beautiful thing is, women don't like her. Look how well I did with women tonight.”

Tellingly, Mary Pat Christie—the first lady of New Jersey—appeared to roll her eyes as she stood behind Trump and listened him. (Her husband stuck to the weird, vacant stare he uses for Trump rallies.)

First, a fact-check: On a basic level, Trump is wrong. As The Washington Post notes, Trump has beaten his Republican rivals among women in the primary so far, by around 10 points overall; he outperformed that mark Tuesday. But that seems to be mostly a factor of his large lead in the race. To say that women particularly like him would be a vast overstatement. Poll after poll has shown that female voters really don’t like Trump. Gallup found this month that 70 percent of women have an unfavorable view of him. In March, Reuters and Ipsos found that half of American women have a “very unfavorable” view of Trump. Suffolk and USA Today recently found him at 66 percent unfavorable among women. (Unsurprisingly, he does better among Republican women than women overall.)

Do women dislike Clinton, as Trump said? They don’t exactly love her, it’s true. Gallup found her at a net negative-3 among women. (Her standing among women has tumbled over the last year in Gallup’s numbers.) Other polls are rosier. George Washington University found 51 percent of women have a positive view versus 47 percent negative. Suffolk found her at 42 favorable and 48 negative.

In other words, it’s not great. But just as Clinton may be getting a bit of a pass on her overall unfavorables because of Trump’s even worse numbers, the same may prove true among women. An election is a choice. Given the option between Clinton and Trump—with his long history of misogynistic comments, accusations of marital rape, and feud with Megyn Kelly—American women say they’d bite the bullet and vote for Clinton, by a 14-point margin in Reuters’s poll.

Not only is Trump wrong, but as Mary Pat Christie’s negative reaction suggests, he may have phrased his answer in one of the worst possible ways. This sort of attack might well work for Trump, if he could tap into resentments about the increasingly central role that gender has played in her campaign. But accusing Clinton of playing the “woman card” is a risky move, for all the reasons that her zinger in Philly suggested: It’s easily turned around into a positive.

But it also might be a counterproductive move for Trump. After studiously shying away from gender for most of her 2008 presidential campaign, Clinton has made it a more central theme of this year’s run, as I’ve written before. In addition to her cabinet pledge, she has noted that she is considering female running mates, and she’s emphasized her credentials as a grandmother and mother—in addition to as a senator and secretary of state.

Suggesting that Clinton is only where she is because she’s a woman won’t sit well with women who are paid less in the workplace, have to fight harder for promotions, and are still badly underrepresented in the top tier of American business and politics. Their experience is not that women get to places where they don’t belong just on the basis of their gender—just the opposite, in fact. Given Clinton’s long, impressive resume, the argument is even harder to buy. (Questioning what, exactly, she has accomplished over the course of that career is fairer, and probably more fertile, ground.)

A close relation of Trump’s argument Tuesday is the claim that Hillary Clinton wouldn’t be where she is without Bill Clinton—that her career is all just a coda to her husband’s. To a certain extent, there may be truth to that: There’s no substitute for the exposure to both publicity and the workings of power that a first lady can get in eight years in the White House. But there have been 45 first ladies, and only one became a senator, secretary of state, and likely presidential nominee afterwards.

It might be more illuminating to reverse the starting proposition: Would Bill Clinton be where he is without Hillary Clinton? It’s very easy to imagine the answer is no. When he first ran for office, in 1972, the couple were not yet married, and he lost. His next campaign was in 1976, after their union, and a win. Biographies show that Hillary was an essential adviser to her husband on both policy and politics. While her signature policy push of the Bill Clinton administration, the 1993 health-care overhaul, was a failure, she was viewed as a powerhouse in Arkansas. After she led a committee devoted to reforming the state’s schools, one dazzled legislator exclaimed, “Gentlemen, we’ve elected the wrong Clinton!” (Clinton aide Betsey Wright later told Connie Bruck that comment wasn’t as benevolent as it seemed: “That was an endearing but sexist statement. They were so amazed that a woman could be so smart.”) In 1992, Bill Clinton liked to say that by electing him president, voters would get “two for the price of one.”

No one is able to tell Trump what to do strategy-wise, and as his success so far shows, he seems to have an intuitive knack for campaigning. Nonetheless, continuing to attack Clinton on “the woman card” doesn’t look like a winning strategy for him in a general-election campaign. Over the course of her long career, Clinton has repeatedly turned sexist and arguably sexist moments into huge political winners. You might even say she wouldn’t have gotten this far without them.