For the first time since the Trump presidency began, President Donald Trump is in some real legal jeopardy, providing potential grounds for his eventual impeachment, if not indictment.

Most people watching the investigations involving Trump and his orbit have been focused on whether special counsel Robert Mueller is going to bring charges related to possible illegal coordination between the 2016 Trump presidential campaign and Russian government entities. But Tuesday brought news of a different kind of campaign collusion: between Trump and his personal lawyer, Michael Cohen. Cohen’s guilty plea to campaign finance violations related to hush money payments to porn actress Stormy Daniels and former Playboy Playmate Karen McDougal brings the president front and center in a conspiracy to violate federal campaign finance laws.

As I laid out in Slate last week, Cohen’s payments of hush money would be illegal, excessive campaign contributions if prosecutors could prove that the payments were made to help Trump’s campaign, not to help Trump with his personal life. The Wall Street Journal reported last week that prosecutors had uncovered evidence that Cohen rebuffed an approach to pay off Daniels in September 2016, but then pursued the payments in October 2016, after the damaging Access Hollywood tape was released and as the campaign was heated and close. This was strong evidence that the payments were campaign-related.

On Tuesday, Cohen pleaded guilty to making these excessive contributions, and to illegally using a corporation to do so. According to a government document, Cohen faces between 51 and 63 months in prison and up to $1 million in fines under the DOJ’s recommended sentencing guidelines for the campaign finance violations and other assorted charges to which he has pleaded guilty. Court documents indicated that much of this work of keeping the women quiet was done in coordination with people at the parent company of the National Enquirer, whose owner David Pecker is a Trump friend and major supporter.

But Cohen did more than admit guilt: In open court he indicated that the payments were made “in coordination with and at the direction of a candidate for federal office” and “for the principal purpose of influencing the election.”

If prosecutors have evidence such as text messages or recordings corroborating Cohen’s statement implicating Trump, that would be more than enough for Trump to be charged with a crime. It is illegal to conspire with someone to make an excessive illegal contribution, and it is illegal for a candidate or campaign to accept an excessive illegal contribution. The same goes for the illegal corporate contributions. As Cohen’s attorney Lanny Davis asked: “If those payments were a crime for Michael Cohen, why wouldn’t they be a crime for Donald Trump?”

Of course, Department of Justice guidance says that prosecutors cannot indict a sitting president. This has never been tested by the courts, though. At the same time, President Trump is about to be given a hand-picked Supreme Court justice in Judge Brett Kavanaugh, who has indicated a desire to expand presidential power and a profound skepticism of investigations of the president.

Trump lawyer Rudy Giuliani’s statement that there is “no allegation of wrongdoing against the President” in the Cohen charges may be technically true, but not enough to help Trump. Court documents indicate that, in making the hush money payments, Cohen “coordinated with one or more members of the campaign, including through meetings and phone calls, about the fact, nature, and timing of the payments.” And Cohen’s admission in open court that he made the payments at Trump’s behest implicates Trump and not just a “member of the campaign.”

It is not surprising that the U.S. attorney has not brought charges against Trump, given the aforementioned DOJ policy that sitting presidents not be indicted for crimes. (Whether or not that is a good policy is a question for another day.) But that doesn’t mean that the government could not prove the crime if it wanted to. “We will not fear prosecuting additional campaign finance cases,” Robert S. Khuzami, deputy U.S. attorney for the Southern District of New York, told reporters after the guilty plea was entered.

More importantly, assuming Cohen’s story can be corroborated with documentary evidence, the campaign finance violations could count as impeachable offenses that the House of Representatives could consider in any articles of impeachment against Trump.

Whether or not Democrats will seek to impeach Trump should they retake the House is a separate political question. If there’s no other uncovered criminal activity, are these hush money payments in violation of campaign finance law bad enough to take down a president, particularly if it would be hard to imagine two-thirds of the Senate agreeing to convict on such grounds? These are political questions for a later date.

Ultimately, Trump may face no penalty, but make no mistake: If Cohen’s story is corroborated, Trump has committed a crime, one that does not depend upon proof of Russian collusion or obstruction.