"It is undeniable -- the Republican Party cannot be both loyal to Donald Trump and loyal to the Constitution. We must choose," Cheney told the crowd.
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"We must not elect people who are more loyal to power or to themselves than they are to our Constitution," Cheney went on to say.
The Wyoming representative spoke at the library's speaker series focused on the future of the Republican party.
She spoke to an audience that received her remarks well.
Cheney is one of just two Republicans on the House committee investigating the Jan. 6 insurrection and has emerged as one of Trump's top critics.
Cheney took pains before addressing Trump and the Jan. 6 committee to reiterate that she holds deeply felt conservative policy beliefs and has long been connected to the party, in part through her father, Dick Cheney, a former secretary of defense and vice president. She also took time to criticize Democratic President Joe Biden's handling of inflation and the southern border.
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"But at this moment, we are confronting a domestic threat we have never faced before -- a former president who is attempting to unravel the foundations of our constitutional republic. And he is aided by Republican leaders and elected officials who have made themselves willing hostages to this dangerous and irrational man," she said.
She also referenced Cassidy Hutchinson, an aide in Trump's White House who testified Tuesday before the House committee that Trump was told that armed protesters were at a rally he led just before the insurrection, and that Trump tried to go with the crowd he encouraged to march on the Capitol.
"Her bravery and her patriotism yesterday were awesome to behold," Cheney said.
ABC News and the Associated Press contributed to this report.