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Washington • Not enough has been made of two obvious facts: Hillary Clinton, if she wins, would be the first woman elected to the White House. And it will have been the votes of women who put her there.

Think, for a moment, about what a remarkable milestone that would be. Consider what it would say about the long and difficult struggle to make the Constitution's guarantees of freedom and equality encompass all Americans. The first 43 presidents were all members of a privileged minority group — white males. The 44th is a black man, and the 45th may well be a white woman. That is a very big deal.

The historic nature of Clinton's candidacy has been all but lost amid the clamorous sound and fury of the Donald Trump eruption. The campaign has seen many unforgettable moments, but one that I believe will prove truly indelible came during the third and final debate, when Clinton was speaking and Trump interrupted her by snarling, "Such a nasty woman."

Within minutes, "nasty woman" became an internet meme — not so much because of what it said about Trump, since we already knew of his sexism and misogyny, but because of what it said about the moment. A "nasty woman" was on the verge of shattering the highest and most shatterproof glass ceiling of them all. That this accomplishment would come at Trump's expense just made it a bit sweeter.

Polls show Clinton leading Trump among women by double-digit margins — an incredible 18 percentage points in a recent Fox News poll. If only men could vote, Trump would have a lead, albeit a shrinking one. But thanks to the 19th Amendment, Clinton is well ahead nationally and has taken solid leads in almost all the swing states.

Surely this has something to do with the "Access Hollywood" videotape in which Trump brags of groping and kissing women against their will — and the 11 women who have come forward to accuse him of doing just that. But I like to believe it also has much to do with Clinton and the virtues she has demonstrated during the campaign.

Trump's slide in the polls, you will recall, began after the first debate, before the "Access Hollywood" tape came to light. The contrast at that encounter, which took place at Hofstra University on Long Island, was striking. Trump was clearly winging it, relying on swagger and presence to bluff his way past questions he could not intelligibly answer. Clinton was sharp and aggressive, but also fully prepared to discuss the issues in detail. She had done her homework, and it showed.

This was the case in the second and third debates as well, and I'll bet her performances struck a chord among women who watched. To succeed, a woman can't just be as good as her male counterparts. She has to be better. She has to know more, she has to work harder, she has to sweat the details while maintaining the illusion that she never perspires at all.

Like any woman who runs for office — or, for that matter, seeks a corner office in the business world — Clinton faced scrutiny in ways men never do. What was she wearing? Did she sound "shrill" — as opposed to "bold" or dynamic" — when she raised her voice? Did she smile enough? Did she smile too much?

Male candidates simply are not critiqued in this manner, unless there is something bizarre about them that cannot be ignored (such as Trump's hairstyle). The next woman nominated for president by one of our major parties will have a lighter burden because of the poise with which Clinton conducted herself and her campaign.

Barack Obama's election meant that African-American parents were no longer lying when they told their children they could grow up to be president. Likewise, if Clinton wins on Nov. 8, all parents will be truthful when they tell their daughters that there is nothing they cannot achieve.

It is ironic that when Bill and Hillary Clinton first met, she was the rising academic and political star, largely on the basis of a 1969 Wellesley College graduation speech that received national attention. But she put her own ambitions on hold in favor of her husband's. It was, at the time, a rational choice; he was likely to go further, and be able to achieve more, than any woman. Only decades later could she step out on her own.

That's a familiar story to millions of women. Now they look ready to change the script.

Eugene Robinson's email address is eugenerobinson@washpost.com.