The House’s public impeachment hearings are underway, with a top State Department official, George Kent, and the top U.S. diplomat to Ukraine, William B. Taylor Jr., testifying Wednesday.

Below are some takeaways from their testimony.

1. A new puzzle piece undermining key Trump defenses

Taylor’s testimony includes something he learned after his Oct. 22 deposition. And it’s significant, because it undermines President Trump’s defenses in several ways.

Taylor said that a member of his staff accompanied Gordon Sondland, the U.S. ambassador to the European Union, the day after Trump’s July 25 call with Ukraine President Volodymyr Zelensky, and that the staff member overheard a phone call between Sondland and Trump.

“The member of my staff could hear President Trump on the phone asking Ambassador Sondland about ‘the investigations.’ Ambassador Sondland told President Trump that the Ukrainians were ready to move forward,” Taylor said.

Taylor added: “Following the call with President Trump, the member of my staff asked Ambassador Sondland what President Trump thought about Ukraine. Ambassador Sondland responded that President Trump cares more about the investigations of [Joe] Biden, which Giuliani was pressing for.”

It’s no surprise that Trump was keen on these investigations; he made that clear on the July 25 call, for which we have a rough transcript. He even mentioned Biden specifically.

But this is significant for a few reasons.

First, it undermines Trump’s claim last week that he wasn’t really familiar with Sondland. “I hardly know the gentleman,” Trump maintained. The fact that Sondland could ring Trump on a cellphone suggests quite the opposite.

President Trump on Nov. 8 said he hardly knows U.S. Ambassador to the European Union Gordon Sondland. (The Washington Post)

Second, it provides a rare window into Trump personally pushing for these investigations, at a time when Republicans are trying to argue that he is not at the core of the Ukraine scandal.

And third, it undermines the idea that Trump was truly concerned about corruption in Ukraine and wasn’t just out for his own personal gain, which has been a chief defense for the Trump team.

One detail: The testimony, however, doesn’t include Trump explicitly talking about a quid pro quo, which we have yet to see from any witness.

2. More explaining to do from Sondland

It’s also notable that Sondland seemed to convey to Trump that they had secured the deliverable.

A big question now is what assurances that might have been based upon, beyond the Trump-Zelensky call, in which Zelensky expressed openness toward the investigations. Sondland’s own deposition doesn’t include this phone call, which is difficult to understand.

Sondland has already clarified his testimony after it omitted details of another key event on July 10. His attorney Robert Luskin told The Washington Post on Wednesday, “Sondland will address any issues that arise from this in his testimony next week.”

3. Taylor cites numerous veiled — but clear — confirmations of quid pro quo

We knew based upon Taylor’s testimony that, even as Sondland passed along Trump’s assurances that there was no quid pro quo, Taylor believed that wasn’t the case.

And under questioning from Democratic counsel Daniel S. Goldman, Taylor made that abundantly clear.

He said that when Sondland told him that there would be a “stalemate” if no investigations were announced, Taylor said he understood that to mean U.S. military aid was conditioned on those investigations.

“What I understood [him as saying] is that security assistance would not come,” Taylor said.

Goldman also asked Taylor about what Taylor has said both Sondland and Ukraine special envoy Kurt Volker passed along to him: that Trump is a businessman and wants to get what is owed to him before he signs a check.

Taylor said he understood the anecdote to mean that Trump believed Ukraine owed him something and needed to deliver it — apparently the investigations — if he were to sign off on the military aid.

“He used that analogy very clearly to indicate that this would require something,” Taylor said. “If that person owed him something, before he signed the check, he was going to get whatever was owed to him.”

Taylor is not a firsthand witness to many of these events, but it’s notable that his testimony suggests many people closer to Trump understood that there was some kind of quid pro quo. And that was reinforced to Taylor on numerous occasions, according to him, including these two.

4. Kent dismisses Trump-Giuliani conspiracy theory

Kent at several points made clear that the conspiracy theory Trump and Giuliani pursued that Ukraine interfered in the 2016 election rather than Russia was not taken seriously.

“To your knowledge, is there any factual basis to support the allegation that Ukraine interfered in the 2016 election?” Goldman asked, to which Kent replied, “To my knowledge, there is no factual basis, no. … I think it’s amply clear that Russian interference was at the heart of the interference.”

Kent also said he wasn’t even familiar with the company Trump cited on his call with Zelensky as being involved in the proposed investigation.

“To be honest, I had not heard of CrowdStrike until I read this transcript on Sept. 25,” Kent said.

That’s significant, because Kent’s job was focused on this region. The idea that he would be unfamiliar with CrowdStrike and saw no basis for this conspiracy theory shows how obscure it was.

5. Painting the view from 30,000 feet

The utility of the two witnesses Wednesday for Democrats is that they can paint the broader picture of a U.S. foreign policy that was hijacked by personal American interests and corrupt Ukrainian — and possibly even American — officials. And two sections of their opening statements drove that home.

In his statement, Kent said: “It was unexpected, and most unfortunate, to watch some Americans — including those who allied themselves with corrupt Ukrainians in pursuit of private agendas — launch attacks on dedicated public servants advancing U.S. interests in Ukraine. In my opinion, those attacks undermined U.S. and Ukrainian national interests and damaged our critical bilateral relationship.”

Taylor echoed that sentiment, pointing to “a rancorous story about whistleblowers, Mr. Giuliani, side channels, quid pro quos, corruption, and interference in elections. In this story Ukraine is merely an object.”

Taylor sought to emphasize, though, as Kent did: “But there is another Ukraine story — a positive, bipartisan one. In this second story, Ukraine is the subject.”

This has been a common thread in the testimony of career officials: ensuring people don’t come to view Ukraine as simply a pawn but, rather, as a vital partner. They’re also apparently seeking to combat GOP attacks suggesting they are deep-state operatives who are out to get Trump.