They did have solid evidence to impeach Trump. He's been impeached.
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Impeachment requires "high crimes and misdemeanors". The articles votes on don't seem to include any statutory crimes making them invalid. Furthermore the articles of impeachment have not been submitted to The Senate, meaning technically until that has been done, the legal prerequisites for an impeachment to be valid have not been completed.
High crime and misdemeanors is the text that's used in the constitution but that doesn't necessarily exclude impeachment for something that isn't a crime. The framers of the constitution presumably anticipated a complex legal framework that would be created after the drafting of the constitution which explains the open ended verbiage of the phrase "high crimes and misdemeanors." That being said, it absolutely should be a precedent in today's legal framework that the President be charged with a specific crime when being impeached to prevent the House holding hostage the executive through endless impeachment inquires. Like I said, Trump was not charged with a crime and this is a bad road to go down.