When all is said and done, the April raids by federal prosecutors targeting Michael Cohen’s office and other premises in Manhattan may be seen as a turning point for Donald Trump’s presidency.

Those raids — and Mr. Cohen’s own malfeasance — opened the door for Robert Mueller, on Thursday, to convict President Trump’s longtime loyalist and personal lawyer of lying to Congress. What the special counsel has gathered since the raids provides the clearest proof yet to the American public that Mr. Mueller’s inquiry — derided by the president and his allies as an aimless fishing expedition — is rooted in the law and facts. To those critics, this latest move was surely meant to send another message as well: He’s not about to back down.

Mr. Cohen’s guilty plea, filed in the same federal courthouse where he already faces a steep sentence for orchestrating campaign-finance and other crimes, brings Mr. Mueller’s operation to New York, the heart of the president’s business empire and the self-made myth that propels it. If there’s anything that plea exposes, it’s that Mr. Trump’s mind never strayed far from his business dealings and how to further enrich himself and his family, even as he was campaigning for the nation’s highest office.

The facts to which Mr. Cohen admitted on Thursday don’t establish that Mr. Trump conspired with Russian efforts to win him the election, but they refute Mr. Trump’s frequent, vehement claim that he had nothing to do with Russia as he sought the White House. It was that falsehood that Mr. Cohen sought to protect by lying himself. “I made these statements to be consistent with” Mr. Trump’s “political messaging,” he said in court.