This view argued by these 45 members of the senate without a conscience is contradicted a lot :
Professor Laurence Tribe disagrees with them
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Concluding otherwise would all but erase the disqualification power from the Constitution’s text: If an impeachable officer became immune from trial and conviction upon leaving office, any official seeing conviction as imminent could easily remove the prospect of disqualification simply by resigning moments before the Senate’s anticipated verdict.
The clear weight of history, original understanding and congressional practice bolsters the case for concluding that the end of Donald Trump’s presidency would not end his Senate trial.
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Just Security disagrees :
.Besides the arguments I have previously made that the Constitution mentions no time barriers on impeachment anywhere in the six clauses defining the process and the dangers of allowing presidents to escape responsibility for misconduct done in or discovered after their last few days in office, there are three other compelling arguments that post-presidential impeachment is legitimate. The first is that a president who returns to private life is not like other private citizens.
Post-presidential impeachment is also legitimate because the Senate rules, initially drafted by Thomas Jefferson when he was vice-president, allow it. They provide that once the Senate has received the articles of impeachment, the Senate must “immediately” proceed with a trial.
Once the Senate receives the articles of impeachment against Trump, the Senate has no choice but to begin an impeachment trial. The third reason that post-presidential impeachment is legitimate is perhaps the most compelling: On three separate occasions after an official left office, Congress proceeded with an impeachment and a trial of the impeached official. These three precedents provide a strong foundation for the Senate’s conducting a second impeachment trial of Trump. Some commentators overlook or dismiss these precedents because they did not involve presidents, but that makes no sense, since there is only one impeachment clause, which subjects presidents and every other impeachable official to the same process: They “shall be removed from office on impeachment for and conviction of treason, bribery, or other high crimes and misdemeanors.”
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.It is nonsensical :
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While the Constitution’s text may be ambiguous, the original understanding and subsequent congressional practice emphatically establish that a former officer is subject to the Senate’s “sole power” to try impeachments. As Alexander Hamilton makes clear in Federalist No. 65, Great Britain provided “[t]he model from which the idea of this institution has been borrowed.” It was firmly established in Britain at the time of the founding that former officers were subject to impeachment. Indeed, the British impeachment that most informed the Framers’ thinking about the impeachment power was the impeachment of Warren Hastings for improprieties as the governor-general of Bengal. Hastings had been out of this office for two years before his impeachment by the House of Commons. Moreover, at least two states—Virginia and Delaware—had established that their impeachment power extended to former officers. Against this background, it is particularly telling that there is no indication in the Federalist Papers or in any other significant commentary from the founding era indicating that the Framers intended the new Constitution to deviate from this baseline understanding.
Congress has also expressly addressed this question and resolved it in favor of the original understanding. In 1876, the House drafted articles of impeachment against President Ulysses S. Grant’s Secretary of War, William Belknap, but Belknap resigned before the House could vote on the articles. The House debated whether Belknap’s resignation deprived the House of jurisdiction. After the debate, the House voted to impeach Belknap, implicitly rejecting the argument that it lacked jurisdiction. The Senate also took up the issue and voted 37–29 that Belknap’s resignation did not deprive it of jurisdiction.
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