Democratic presidential hopefuls argued, praised each other, apologized, refused to apologize and then ultimately agreed that none of it was as important as beating President Donald Trump next year at the ballot box.

The primary debate in Los Angeles, with a more manageable seven candidates onstage, offered the contenders a chance to define themselves more clearly and to distinguish themselves in the field – though none emerged as a clear leader after the debate.

Held six days before Christmas and just a day after Trump suffered the ignoble distinction of being the third U.S. president in history to be impeached, the debate didn't hold the promise of drawing widespread attention from voting Americans. But unlike in earlier debates, candidates at least had a chance to talk about their own campaign messages and challenge those of others.

Former Vice President Joe Biden underscored his experience and the threat he poses to Trump, noting that the president has made a point of going after the former vice president's family. Entrepreneur Andrew Yang turned many questions to technology, noting that the Chinese have developed facial recognition technology to identify protesters and punish them.

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Sen. Elizabeth Warren of Massachusetts, whose Senate career and campaign has centered on corruption, brought that issue up repeatedly – including challenging South Bend, Indiana, Mayor Pete Buttigieg on the issue. Activist billionaire Tom Steyer reminded people he had been pro-impeachment before it was cool with the Democratic leadership, Buttigieg and Sen. Amy Klobuchar of Minnesota touted their Midwestern roots, and Sen. Bernie Sanders of Vermont cast himself as the candidate who started the progressive romance with "Medicare for All," climate change action and campaign finance reform.

Things got testy when it came to two issues Democrats see as defining for the party: racial and gender equality, and rejecting big money to pay for campaigns. Buttigieg, who is doing well in polls in Iowa, took the brunt of the criticism.

A question from the panel was deliberately provocative: Former President Barack Obama recently commented that the world was run by a lot of old white men – and that if they got "out of the way" and women ran things, the world would be a better place. What are your thoughts, one of the moderators asked – starting with two older white men.

Sanders, identified as the oldest of the Democratic contenders, bristled at the query.

"And I'm white, too!" the Vermont senator said, interrupting the question. "I disagree with him on this one," Sanders said, referring to Obama. "Maybe a little self-serving, but I do disagree."

Power disparities in America are not about "white or black or male or female," Sanders said, but in the fact that "we are increasingly becoming an oligarchy." Sanders then turned the question to Medicare for All.

Biden, the second-oldest white male onstage, got the question next.

"I'm going to guess he wasn't talking about me either," the former vice president quipped about the man he served with in the White House. As for his age, Biden said he would not commit to running for a second term if he's elected – but won't rule it out either. "Let's see what happens," he said.

Klobuchar – after thanking the panel for "asking a woman this question" – said she "would be so proud to be the first woman president, but mostly I want to be a president who gets things done." And Warren – after being reminded that she, too, would be the oldest president ever inaugurated – earned a round of applause when she noted that she also would be the youngest woman ever inaugurated.

Yang, as the only person of color onstage, said he was disappointed that he was not joined by the likes of Sen. Cory Booker of New Jersey and Sen. Kamala Harris of California. Booker did not meet the polling thresholds to make the debate stage and Harris, citing fundraising problems, recently dropped out of the race. The screening process meant that the most diverse presidential candidate slate in history was not reflected on Thursday's debate stage.

Tempers flared, too, when the candidates tussled about fundraising and the experience needed to serve as president. Warren mentioned she didn't do big-dollar fundraisers, which Buttigieg took as a shot at him. That led to an ancillary feud over Buttigieg's closed fundraisers and candidates competing over who had the smallest average donations.

"We're in the fight of our lives right now," the South Bend mayor said. "I'm the only person on this stage who is not a millionaire or billionaire. This is the problem with issuing purity tests you yourself cannot pass." Steyer, who is a billionaire and not seeking donations, metaphorically threw up his hands.

"There's someone who is loving this conversation, and his name is Donald Trump," Steyer said.

Klobuchar – who was arguably more dominant and confident than in any of her other debate appearances – clashed with Buttigieg, too, on the issue of experience, challenging what she saw as a dismissive description of her work as serving on committees.

The Minnesota lawmaker first noted the accomplishments of some of her competitors who served in the Senate, mentioning Warren's fight for the Consumer Financial Protection Bureau, Biden's fight for cancer funding, Sanders' work for veterans and her own negotiations on farm bills. "I just think you should respect our experience," she said.

Biden, in a separate question, defended comments he made earlier in the campaign that he is capable of working with the Republicans who are now so at odds with Democrats in Congress.

"I refuse to accept the notion, as some on this stage do, that we can never, never get to a place where we have cooperation again," Biden said, repeating language he has used on the campaign trail. "If that's the case, we're dead as a country.

"If anyone has reason to be angry with Republicans and not want to cooperate, it's really me – the way they've attacked me, my son, my family," Biden added, a not-so-veiled reference to how much Trump worries about running against him. "I know we have to … be able to get things done."

The contenders also revisited past feuds over the plausibility of their proposals, with Biden's voice rising as he slammed Sanders' health care plan – which Biden said would cost $30 trillion and raise taxes – as too expensive and unworkable. Buttigieg said Warren's plan to eliminate tuition at public colleges was not a benefit that should be afforded to wealthier families.

Largely, though, the contenders agreed on goals – making prescription drugs more affordable, helping immigrants and bringing a sense of decency back to Washington. Asked to choose a closing message – offering a gift or asking for forgiveness – the two women both asked for forgiveness.

Warren and Klobuchar said they apologized for their passion on the campaign trail.