The house is not included in this fake impeachment because, so far, there is no vote whether or not a vote is 'constitutional' is an empty argument. That means, the impeachment proceedings are being done by a few Democrats. Pelosi knows that impeachment is political suicide for her party but pretending to 'inquire' into an impeachment may give them political advantage.
There are no 'impeachment proceedings' right now- there is an impeachment investigation.
Once the investigation is complete I think we will see a vote.
So far the facts we have are:
a) The President has asked two foreign governments to investigate his political opponents
b) The President(according to his own Chief of Staff) at least in part held up Congressionally authorized military assistance to Ukraine until Ukraine agreed to investigate the President's personal interest- the DNC's server- a quid pro quo.
c) We now have the President using his Presidential authority to direct business to his own business.
d) And there is still obstruction of justice on the table.
Any of those- and probably all of those- will be on the impeachment vote.