The Senate impeachment trial of former President Donald Trump officially began Tuesday afternoon, and presiding officer Patrick Leahy, D-Vt., promised to conduct the proceedings fairly.

Normally, as was done with Trump's first impeachment trial and that of former President Bill Clinton, the chief justice of the Supreme Court presides over a presidential impeachment trial. As Trump is no longer president, Leahy – the president pro tempore of the Senate – is filling that role.

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"As many of you know, I did not ask or seek to preside over this trial," Leahy wrote in a letter to the Senate on Tuesday. "Yet while I occupy the constitutional office of the President pro tempore, it is incumbent upon me to do so."

Leahy assured his colleagues that while he may be of the same party as the Democratic House impeachment managers prosecuting the case, he will look to rules and precedent for how to decide any questions that may arise.

"My intention and solemn obligation is to conduct this trial with fairness to all," Leahy said. "Should a motion, objection, request, or application related to the procedure of the Senate or to the trial be put before me, I will consult with the Parliamentarian and be guided by Senate precedent."

Leahy also said that any decision he makes will be up for review by the entire Senate and that he would submit any constitutional question to the full Senate as well.

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One such constitutional question is the Senate's main focus on Tuesday afternoon: whether a president can face a Senate impeachment trial after being removed from office. Trump and other Republicans say no, claiming that a process primarily meant to oust an official from office cannot be used for a private citizen who no longer holds that office.

Democrats have claimed that a trial is proper because another possible outcome of an impeachment trial is to disqualify someone from holding office in the future. During his opening statement, House impeachment manager Rep. Jamie Raskin, D-Md., claimed that exempting Trump would provide a "January exception" that would allow presidents to commit offenses at the end of their term without facing consequences.

Leahy addressed the gravity of the situation and his role in it days after he assumed the president pro tempore position.

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"When presiding over an impeachment trial, the president pro tempore takes an additional special oath to do impartial justice according to the Constitution and the laws.  It is an oath that I take extraordinarily seriously," he said in a statement, adding that he "will not waver from my constitutional and sworn obligations to administer the trial with fairness, in accordance with the Constitution and the laws."

"The president pro tempore has historically presided over Senate impeachment trials of non-presidents," Leahy said in a statement announcing his new role. "When presiding over an impeachment trial, the president pro tempore takes an additional special oath to do impartial justice according to the Constitution and the laws. It is an oath that I take extraordinarily seriously."