The House of Representatives has undertaken the impeachment inquiry of a president only four times in American history. Each time, the House has set its own ground rules. The Constitution prescribes no specific process, nor does federal law. Court rulings and precedents, such as they are, tend to be narrow and particular. So when lawmakers determine that such a proceeding is warranted, they are forced to rely on their own cobbled-together rule book, with the trust of the American people in their government at stake.

This requires Congress to be rigorous in setting out the rules for conducting an inquiry. It also makes the impeachment process vulnerable to misrepresentation and caricature, as President Trump and his White House demonstrated on Tuesday. According to an astonishing letter from the Trump administration to House Democrats, it is right for the president of the United States to use his immense power to solicit a foreign government’s interference on his behalf in an election — even, possibly, by way of extortion. At the same time, the letter argued, it is illegitimate for Congress, a coequal branch of government, to undertake any investigation into the president or members of his administration (or diplomats, personal lawyers and hangers-on) regarding this behavior.

The letter is a formal assertion of executive power and impunity without precedent in American history. Or, as a former Republican Senate staff member wrote on Twitter: “Wow. This letter is bananas.”

Take the first claim first, that there is nothing wrong with Mr. Trump shaking down a foreign leader for his own political benefit. Perhaps that’s the only position the White House can take, because the facts of the July 25 call are not in dispute. The administration’s own written summary of the conversation reveals that Mr. Trump pressured Volodymyr Zelensky, the Ukrainian president, to investigate former Vice President Joe Biden, a top political rival, and his son Hunter for supposed corruption. At the time of the call, Mr. Trump was withholding nearly $400 million in promised military aid to Ukraine — a topic that was alluded to in connection to his requests that Mr. Zelensky “do us a favor.”