WASHINGTON — President Barack Obama and the first lady, Michelle Obama, issued scathing denunciations of Donald Trump on Wednesday, arguing that Trump keeps offering more proof that he is unfit to be president.

In a radio interview Wednesday morning, Obama lashed out at the Republican presidential nominee for denigrating women and mocked Trump’s debate appearance, saying it exposed him as a person who “appears to only care about himself.”

Obama described Trump as someone who was unqualified to sit in the Oval Office and “doesn’t do his homework, doesn’t know basic facts that you’d need to know.”

“You had somebody who basically insulted women and then doubled down,” Obama told Steve Harvey, a syndicated radio host. “In terms of how he talks about them and talks about their weight and talks about how they look instead of the content of their character and their capabilities, which is not something that I want, not somebody I want in the Oval Office.”

Hours later, in the first of two appearances Wednesday for Hillary Clinton, the Democratic nominee for president, the first lady tore into Trump without ever using his name.

“If a candidate is erratic and threatening; if a candidate traffics in prejudice, fears and lies on the campaign trail; if a candidate thinks that not paying taxes makes you smart, or that it’s good business when people lose their homes; if a candidate regularly and flippantly makes cruel and insulting comments about women, about how we look, how we act — well, sadly, that’s who that candidate really is,” Michelle Obama told an audience of mostly students at La Salle University in Philadelphia. “That is the kind of president they will be.”

Michelle Obama, who was to deliver an address in Pittsburgh later in the afternoon, prompted laughter when she acknowledged that Clinton had seen the presidency “from every angle — the staggering stakes, the brutal hours, the overwhelming stresses” and still wanted to do the job.

The president and Michelle Obama stressed the need for Democrats to turn out in force for Clinton and not to waste their vote by casting ballots for third-party candidates with little chance of winning.

“You could also help swing an entire precinct for Hillary’s opponent with a protest vote or by staying home out of frustration,” Michelle Obama said. “Because here’s the truth: Either Hillary Clinton or her opponent will be elected president this year. And if you vote for someone other than Hillary, or if you don’t vote at all, then you are helping to elect Hillary’s opponent.”

Barack Obama also implored his supporters to make sure they voted for Clinton and insisted repeatedly that anyone who failed to vote in November, or who voted for a third-party candidate, was effectively casting a ballot for Trump.

“If you don’t vote, that’s a vote for Trump,” the president said. “If you vote for a third-party candidate who has got no chance to win, that’s a vote for Trump.”

White House officials have always known that one of Obama’s principal tasks in the final weeks of the campaign would be to help energize the coalition of voters — especially young people and African-Americans — to support Clinton in large numbers. With the contest close in many battleground states, that effort is taking on added urgency.

Obama urged those supporters not to be complacent.

“The notion somehow that I’m not as inspired because Barack and Michelle are not on the ballot this time, and maybe we kind of take it easy,” he said. “My legacy is on the ballot. All the work we’ve done over the last eight years is on the ballot.”

Obama praised Clinton, calling her “as qualified as anybody who’s ever run for this office” and expressing frustration that people have not given her the credit she deserves for her accomplishments.

“Part of it may be because she is a woman and we have not elected a woman president before,” he said.

But he spent more time criticizing Trump.

Obama accused him of “rooting for the housing market to collapse because he would be in a position to buy up all of these properties.” He said he did not want someone in the presidency whose “only focus is how can I make a buck off it.”

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