Rudy Giuliani lied about a Trump Tower Moscow letter of intent. CNN has receipts.

On Tuesday evening, CNN host Chris Cuomo announced that the network has obtained a letter of intent personally signed by Donald Trump to proceed with a lucrative Trump Tower Moscow project that would have provided his company with a $4 million upfront fee.

Cuomo brandished the document on his show and highlighted how it contrasts with what Trump’s lawyer, Rudy Giuliani, said as recently as Sunday, when he told CNN that Trump Tower Moscow “was a real estate project. There was a letter of intent to go forward, but no one signed it.”

Giuliani’s claim is incorrect. It turns out Trump himself signed the letter of intent, which is dated October 28, 2015 — five months after Trump launched his presidential campaign, and during a period in which he was lavishing praise on Russian President Vladimir Putin.

Trump’s longtime lawyer, Michael Cohen, told Congress last year that Trump signed the document. CNN has now published proof.

CNN reports that the non-binding letter of intent — also signed by Andrey Rozov, owner of the Russian firm that would have partnered with the Trump Organization on the project, I.C. Expert Investment Co. — outlined a deal that would have given Trump’s company “a $4 million upfront fee, no upfront costs, a percentage of the sales and control over marketing and design. The deal also included an opportunity to name the hotel spa after Trump’s daughter Ivanka.”

Even though he personally signed a letter of intent for Trump Tower Moscow, Trump repeatedly claimed during his campaign that he had “nothing to do with Russia” and “I know nothing about Russia ... I don’t deal there.”

During a news conference held days before his inauguration, Trump offered a comment that now seems especially dubious in light of the signed letter of intent.

“I have no dealings with Russia, I have no deals in Russia, I have no deals that could happen in Russia because we stayed away,” Trump said. “We could make deals in Russia very easily if we wanted to. I just don’t want to because I think that would be a conflict. So I have no loans, no dealings, and no current pending deals.”

Trump has already tried to rewrite this history. After Cohen agreed to a plea deal with special counsel Robert Mueller last month that acknowledged he made false statements to Congress about the Trump Organization’s dealings with Russia, Trump claimed “everybody knew” about his secret business dealings with Russia. In a tweet posted November 30, Trump even characterized his dealings as “very legal & very cool.”

“I talked about it on the campaign trail,” Trump said, falsely, before adding that he “Lightly looked at doing a building somewhere in Russia.”

During a question-and-answer session with reporters on November 29, Trump referred to the letter of intent but suggested he never signed it.

“I don’t even remember it,” Trump said.

In tweets posted that same day, Trump hinted at a line new of defense — that even if he didn’t tell the truth about his dealings with Russia, lying is not a crime, and therefore the Mueller investigation “is an illegal Hoax that should be ended immediately.”

The president has also emphasized that the deal didn’t end up happening in the end. “I didn’t do the project, I decided not to do the project, so I didn’t do it,” he said on November 29.

Indeed, the letter of intent Trump signed states that “The Parties agree that unless and until a License Agreement between the Parties has been executed and delivered, no party shall be under any legal obligation of any kind whatsoever to consummate a transaction hereby by virtue of the (letter of intent).” There’s no evidence that a License Agreement was ever consummated.

But as Cuomo highlighted during his show on Tuesday evening, legal defenses are one thing — lying to voters about your business dealings with a foreign adversary during a presidential campaign in which that adversary is interfering in the election on your behalf is another.

“Why are they doing this?” Cuomo said, referring to the disconnect between Giuliani’s comment that “no one signed” the letter of intent, and the document affixed with Trump’s signature. “This doesn’t matter legally, and that’s the point — they’re not preparing for trial. Don’t examine it that way. They are preparing for a PR campaign to convince you of what they want you to believe.”

After CNN obtained the letter of intent signed by Trump, Giuliani told the New York Daily News that the letter is “bullshit because it didn’t go anywhere.”

“That was the end of it,” he added. “It means nothing but an expression of interest that means very little unless it goes to a contract and it never did.”

Giuliani also flatly denied saying what he said on Sunday, when he told CNN that “no one signed the letter.”

“I don’t think I said nobody signed it,” Giuliani said to the Daily News.