The Clintons weren't the only former residents of the White House present for the event

“This is not an easy day for anyone that supported her or believes in progressive values, let alone her,” a longtime aide tells PEOPLE. “But she did it, because she’s Hillary Clinton, and she’s there for all the right reasons, honoring democracy, and representing the values she ran on.”

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The former Democratic candidate shared on Twitter that she was attending the swearing in ceremony.

“I’m here today to honor our democracy & its enduring values,” she wrote. “I will never stop believing in our country & its future.”

Image zoom Manuel Balce Ceneta/AP

Though Trump notably didn’t mention Clinton in his inaugural address, he took time out at his luncheon to thank her and her husband for attending his inauguration, urging the attendees to stand up and applaud the former first couple.

The Clintons sat near first daughter Tiffany Trump during the luncheon, and the former secretary of state shook Trump’s hand at one point.

“I was very honored — very, very honored — when I heard that President Bill Clinton and Secretary Hillary Clinton were coming today and I think it’s appropriate to say and I’d like you to stand up,” he said, joining in as the audience clapped. “And honestly there’s nothing more I can say because I have a lot of respect for those two people so thank you all for being here.”

Former presidents traditionally attend the ceremonial transfer of power at the U.S. Capitol, and the Clintons weren’t the only former residents of the White House present for the event.

Image zoom Joe Raedle/Getty

Image zoom Joe Raedle/Getty

Image zoom Joe Raedle/Getty

Image zoom John Angelillo-Pool/Getty

Former president Jimmy Carter has also arrived with his wife, Rosalynn.

Image zoom Joe Raedle/Getty

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Other notable attendees included Trump’s Republican party opponents Marco Rubio, Chris Christie and Ted Cruz, as well as Bernie Sanders, who was defeated by Clinton in the Democratic primary election.

Trump pulled off a surprise victory over Clinton in the general election on Nov. 8, stunning many who expected to see Clinton deliver here victory speech below a literal glass ceiling in Midtown Manhattan.

Instead, Trump confirmed in his victory speech around 2 a.m. the following morning that Clinton had called him to concede. Later in the day she delivered a public concession speech, and urged Americans to support a peaceful transition of power.

“I hope that he will be a successful president for all Americans,” she said of Trump. “We owe him an open mind and the chance to lead.”