WASHINGTON - Hillary Rodham Clinton claimed the standard of the Democratic Party on Tuesday night, declaring victory in her fight for the party's presidential nomination and history as the first female to do so.As the first woman ever nominated to run for president under the banner of a major American political party, Clinton thanked her supporters for her success: "It belongs to generations of women and men who struggled and sacrificed to make this moment possible," she said in a speech from Brooklyn on Tuesday night."We are all standing under a glass ceiling right now," she said from the Brooklyn Navy Yard's Duggal Greenhouse. "But don't worry– we're not smashing this one. Thanks to you, we've reached a milestone: The first time in our nation's history that a woman will be a major party's nominee."Clinton said she wished that her mother, who died in 2011, were still alive to witness the moment. "She taught me never to back down from a bully, which it turns out was pretty good advice," the candidate said.Clinton's campaign now pivots to the general election against Donald J. Trump, the Republican Party's presumptive nominee. But her rival in the Democratic primaries, Senator Bernie Sanders of Vermont, has yet to drop out of the race, and has previously vowed to take his fight for the nomination all the way to the party's convention in Philadelphia next month.Clinton maintains a substantial lead over Sanders in the primary popular vote and in pledged delegates toward the nomination. Paired with enough "super delegates" who have voiced their support for Clinton to reach the party's nomination threshold, several US media outlets declared her the presumptive Democratic nominee on Monday night."This election is different," Clinton said. "It really is about who we are as a nation. It's about millions of Americans coming together to say, we are better than this. We won't let this happen in America.""And if you agree," she continued, "whether you are a Democrat, Republican or Independent, I hope you will join us."