Nancy Pelosi—the first woman to serve as speaker of the House—echoed her colleague later in the proceedings. “We are preparing to shatter the highest glass ceiling in our country,” she said. “Aren’t you proud to be part of this historic moment in our history?”

The metaphors are physical—it’s no accident that Pelosi and Mikulski spoke of barriers and ceilings. There are so many ways in which women in America feel contained, restrained, and limited, whether it’s the smaller amounts they’re paid compared to men, the way their contributions to family life and caregiving are undervalued in American culture, or the pitifully small number of public offices they hold compared to men, especially on the national level. Mikulski has only 19 female colleagues in the United States Senate, and Pelosi 83 in the House; that’s 20 percent of each chamber, and 20 percent of Congress overall.

These two women, Pelosi and Mikulski, are of Clinton’s generation—one for which this nomination is particularly significant. When each legislator was elected to her current position, in the 1980s, there had been little precedent set by others of their gender—it was not assumed that women could, should, or would be elected to the offices long held by men, simply because it hadn’t happened. For a long time, this has been true of the United States presidency, as well: While the world’s Thatchers and Merkels and Gandhis and Meirs might make it seem inevitable that a woman will eventually make it to the White House, this country has thus far offered no evidence that it is possible. Clinton changed that.

The true test of Clinton’s achievement, and the historical nature of this moment, is not whether it’s an automatic salve for all the problems that still disproportionately affect women in America. Just as President Obama’s election did not “fix” race, so Hillary Clinton’s, if it comes to pass, will not “fix” gender. Michelle Obama knows that well; as she said during her speech on Monday night, she wakes up every day in a house built by slaves.

But she also said this: “Because of Hillary Clinton, my daughters and all our sons and daughters now take for granted that a woman can be president of the United States.” That assumption—taking for granted that the the highest political office in the land is fair game for people of all sexes and genders—is what divides Pelosi’s generation from Sasha and Malia’s. It may start to change politics in America.

Tuesday night’s proceedings in Philadelphia became a time for women to cheer their own. Iowa’s delegation touted itself as “a state of female firsts,” citing the University of Iowa’s 1857 acceptance of a woman—the first for a state university in America—and the achievement of Arabella Mansfield, the first woman in the country admitted to the bar. Rhode Island cheered Gina Raimondo, its first female governor, and Minnesota even brought up Walter Mondale, the first person to put a woman—Geraldine Ferraro—on a major national ticket. As the states went through roll call, many, many of them announced their pride in casting ballots for “the first woman president of the United States!”

The possibility of a woman in the White House is now more concrete, more tangible, than it has ever been in American history. But what will truly be worth celebrating, years from now, is when a woman presidential candidate is just normal, her gender not so noteworthy at all.

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