WASHINGTON—From the women’s suffrage movement to the women’s liberation movement to this overdue moment in Brooklyn: a beaming woman on stage, triumphant, speaking as a party nominee for president of the United States.

Hillary Clinton claimed victory in the Democratic presidential primary on Tuesday night with a speech in which she linked her achievement to the previous gains of the U.S. battle for women’s rights. Eight years to the day after a concession speech in which she thanked her voters for making “18 million cracks” in the “highest, hardest glass ceiling,” she celebrated the biggest dent ever made.

“It may be hard to see tonight, but we are all standing under a glass ceiling right now,” she said to raucous cheers.

“Tonight’s victory is not about one person,” she said. “It belongs to generations of women and men who struggled and sacrificed and made this moment possible.”

No woman had won the nomination of a major party in the 240 years since America’s founding. Clinton, who earned more than 13 million votes, now embarks on a general election campaign against Republican nominee Donald Trump. To become the first female president, the first female nominee will have to defeat a man with a long history of sexist remarks who says “the only thing she’s got is the woman’s card.”

Clinton, the former secretary of state, senator and first lady, has spent much of her career fighting for women’s causes — and navigating the delicate politics of gender. Determined to convince male voters of her readiness as commander-in-chief, she rarely mentioned her womanhood in 2008. This time around, she has eagerly embraced her status as a pioneer.

“Don’t let anyone tell you that great things can’t happen in America. Barriers can come down. Justice and equality can win,” she said.

Trump welcomed her to the race with an attack on her ethics. Speaking at his golf course outside New York City, he accused Clinton and her husband, former president Bill Clinton, of “corrupt dealings,” saying they had “turned the politics of personal enrichment into an art form for themselves.” Promising “real change, not Obama change,” Trump painted Hillary Clinton as an “extension of the Obama disaster.”

Clinton responded by calling him “temperamentally unfit” to lead the nation or its military. The election, she said, “is about millions of Americans coming together to say: we are better than this. We won’t let this happen in America.”

Clinton had actually clinched the nomination on Monday, but in the most anticlimactic possible fashion: an Associated Press announcement on Twitter. She had declined to acknowledge her accomplishment until she had achieved not just a majority of all delegates but a majority of “pledged” delegates she had to earn through the voting process.

Her caution was in part designed to maximize her time in the prime-time spotlight. But it was also an effort to avoid irking the loyal supporters of her vanquished rival, Vermont Sen. Bernie Sanders, many of whom believe their candidate’s assertion that the system is “rigged” against them.

Her first general-election task is securing Bernie’s army. Sanders, a longtime independent who has little loyalty to the Democratic establishment, has resisted the suggestion that he should soon drop out of the race, instead vowing to force a “contested convention” by continuing to woo elite superdelegates.

“We are going to fight hard to win the primary in Washington, D.C., and then we take our fight for social, economic, racial and environmental justice to Philadelphia!” he said to a roaring California crowd at 10:40 p.m. local time (1:40 a.m. EDT). “The struggle continues.”

But he will now face immense party pressure to drop out of the race. Obama, who will meet with Sanders at the White House on Thursday, has hinted he will endorse Clinton as early as later this week. Even Sanders’s lone supporter in the Senate, Oregon’s Jeff Merkley, has urged Sanders to give way. And Sanders left himself an opening, saying, “We will not allow Donald Trump to become president of the United States.”

Trump, speaking with the aid of a teleprompter four days after boasting that he doesn’t need such speaking assistance, made a direct appeal to Sanders voters who feel let down by a “rigged system.” But Clinton used part of her speech to offer an olive branch of her own, praising his “extraordinary campaign” and his “long career in public service fighting for progressive causes and principles.”

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“Let there be no mistake: Senator Sanders, his campaign and the vigorous debate that we had … have been very good for the Democratic Party and for America,” she said.

Clinton holds a narrow lead over Trump in the polls, about two percentage points, and was already enjoying a banner month before Tuesday. After clinching the Republican nomination in early May and rapidly consolidating the support of nearly the entire party elite, Trump created another party crisis this week with an unrelenting series of racist attacks on the impartiality of a Hispanic federal judge who is handling a lawsuit against him.

In a Tuesday statement, Trump repeated his suggestion that the judge is not being fair to him because of his Mexican heritage. But he also promised not to discuss the matter again.

“I understand the responsibility of carrying the mantle, and I will never, ever let you down,” he said in his address.

Six states voted in Democratic primaries on Tuesday: New Jersey, California, Montana, New Mexico, North Dakota and South Dakota. The candidates had spent almost all of their time in California, by far the biggest prize. The results there were not yet known late Tuesday; they matter only to the extent that they affect Sanders’s approach to the coming weeks.

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