Meet the new Barack Obama: Her name is Hillary Clinton.

As Democrats transfer their allegiance from the candidate of “Yes We Can” and the rallies with hundreds of thousands to the candidate of the understated YouTube campaign kickoff and the small roundtable discussion, they may think they are giving up the kind of soul-stirring speech that sends partisan hearts fluttering.

But in the first speech of her nascent campaign, Clinton seemed to be borrowing a rhetorical page from her one-time opponent, who on the 2008 campaign trail placed his own candidacy within the larger American struggle for justice.

Speaking to a friendly crowd at the Women in the World Summit in Manhattan, Clinton thundered about the rights and opportunities, political or otherwise, of women and girls around the world.

“It is hard to believe that in 2015 so many women still pay a price for being mothers. It is also hard to believe that so many women are also paid less than many for the same work, with even wider gaps for women of color,” Clinton said to sustained applause. “And if you don’t believe what I say, look to the World Economic Forum, hardly a hotbed of feminist thought. Their rankings show that the United States is 65th out of 142 nations and other territories on equal pay.

“We should be No. 1.”

Clinton placed women’s struggle for equality within the struggle for a more equal economic playing field, pointing out that the lack of parity on wages meant that families had less to spend on education, health care, and retirement.

“When women are held back, our country is held back. When women get ahead, everyone gets ahead,” Clinton said.

“Our mothers and sisters and daughters are on the front lines of all of these battles,” Clinton added later. “But these are not just women’s fights. These have to be America’s fights and the world’s fights. We have to take them on, we have to win them together.”

And although it remains unclear what role her husband, Bill Clinton, will play in her presidential campaign, two other figures of the extended Clinton family may get top billing: her baby granddaughter, who was mentioned 90 seconds into Clinton’s speech and brought up several times thereafter, and Clinton’s own mother.

Dorothy Rodham, as Clinton described her, survived a difficult childhood by relying on the kindness of strangers and acquaintances. She died in 2011 at 92.

“How could you have survived?” Clinton asked. “How could you have built a family of your own, taking such good care of your children?”

The speech was part of the Women in the World Summit, hosted by Daily Beast founding editor Tina Brown, and will last three days at the David Koch Theater at Lincoln Center.

Just as in Clinton’s announcement video, which seemed to include all manner of member of the Democratic coalition—a gay couple readying to marry, a senior citizen preparing to retire, an immigrant entrepreneur starting a new business—Clinton paid tribute to the vast mosaic of issues that face womenkind, including gay and transgender women, undocumented women (she called directly for a “pathway to citizenship”), and women facing sexual assault on campus and in the military. She mentioned the legions of fast-food workers who went on strike and marched in the streets last week in the fight for a higher minimum wage, and she drew parallels between that fight and the fight for greater equality that she witnessed around the world as first lady and later secretary of state.

Clinton also made a thundering denunciation of unnamed Republican opponents, whom she accused of stalling women’s progress.

“We have to have leaders who recognize that the time has come. There are those who offer themselves as leaders who take a very different view,” Clinton said. “There are those who offer themselves as leaders who see nothing wrong with denying women equal pay. There are those who offer themselves as leaders who would defund the country’s leading provider of family planning and want to let health insurance companies once again charge women just because of our gender. There are those who offer themselves as leaders who deport mothers working to give their children a better life rather than face the ire of talk radio. There are those who offer themselves as leaders who would even play politics with the nomination of our nation’s chief law enforcement officer.”

When Obama would succumb to such rhetorical flourishes, he would often reference the grand sweep of history that saw rebels overthrow the British, settlers set out for the West, slaves run away for their freedom, immigrants sail for unknown shores, and African Americans conduct lunch counter sit-ins in the segregated South. That sweep included voters going to the polls to make history themselves and vote for him as president.

At Lincoln Center, Clinton said much the same thing.

“By coming here and being a part of this extraordinary conference, you now must be an agent of change, as well,” Clinton said. “It is up to all of us to be part of the progress we want to see.”

“I am confident,” she added, “that if we get to work, we will get it done, together.”