If it is true that...

The House of Representatives chooses their Speaker and other officers and has the sole power of impeachment

and

The vice president is the president of the Senate but has no vote unless they are equally divided

Then it must be true that...

The senate has the sole power to try all impeachments

If it is true that...

The senate has the sole power to try all impeachments

Then it must be true that...

Judgment in cases of impeachment extends to removal from office and disqualification to hold any office under the United States