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4 takeaways from latest impeachment witnesses, Fiona Hill and David Holmes

Washington(CNN) House Democrats wrapped up their week of marathon impeachment hearings Thursday, with two more witnesses who further corroborated the allegations that President Donald Trump used his powers to pressure Ukraine's leader for political favors.

Lawmakers heard testimony from Fiona Hill, formerly the top Russia expert at the White House, and David Holmes, a career State Department official who works at the US embassy in Ukraine.

The proceedings Thursday were the last public impeachment hearings on the schedule -- for now. Here are four big takeaways from the daylong affair.

Hill took a baseball bat to GOP conspiracies

Hill forcefully rejected and dismantled a handful of Trump-backed conspiracy theories, chiefly the notion that Ukraine meddled in the 2016 election to prevent his presidency. In Hill's opening statement, she called out "some of you on this committee" who spread the discredited theory.

"This is a fictional narrative that has been perpetrated and propagated by the Russian security services themselves," Hill told lawmakers in her opening statement, referring to the allegations that Ukraine meddled in 2016 to harm Trump. "I refuse to be part of an effort to legitimize an alternate narrative that the Ukrainian government is a US adversary, and that Ukraine, not Russia, attacked us in 2016."

She didn't mention Trump by name, but her comments were a clear rebuke of the President. He has promoted these theories about Ukraine meddling and discounted well-founded conclusions about Russian meddling, since the day the Russian hacks became public in June 2016.

This testimony is unlikely to sway GOP lawmakers, some of whom said after the hearing that they still believe the theories. Rep. Scott Perry, a Pennsylvania Republican, told CNN that Hill "is welcome to her opinions" but he still had questions about supposed Ukrainian interference.

She said a 2016 op-ed from the Ukrainian ambassador to the US, where he condemned Trump's comments that Russia could keep Crimea, was "ill-advised" but not uncalled for.

"I could list a whole host of ambassadors from allied countries who tweeted out, who had public comments, about the president," during the 2016 presidential campaign, Hill said, "and it did not affect security assistance, having meetings with them. If it would, there'd have been a lot of people he wouldn't have met with."

She also said a January 2017 Politico article about contacts between lower-level Ukrainian officials and a Democratic operative provided "little evidence of a top-down effort by Ukraine." Republicans repeatedly held up this article as proof that the Ukrainian government undermined Trump's candidacy. Hill rejected those comparisons and said Russia meddled to help Trump.

The Biden-Burisma connection was obvious

Both Hill and Holmes testified Thursday that it was obvious to them that when Trump's aides mentioned "Burisma," a Ukrainian energy company, that they were really thinking about former Vice President Joe Biden. While Biden oversaw the Obama administration's policy toward Ukraine, his son Hunter Biden had a high-paying job serving on the board of Burisma.

"It was very apparent to me that that was what Rudy Giuliani intended, yes, intended to convey that Burisma was linked to the Bidens and he said this publicly repeatedly," Hill said.

For his part, Holmes testified that he understood that "Burisma" was code for the "Bidens." He knew of the desire for investigations through his diplomatic role at the US embassy in Kiev.

They figured it out. But two Trump-appointed diplomats, Gordon Sondland and Kurt Volker, told the committee that they didn't make the connection while they were dealing with Trump's lawyer Rudy Giuliani or pressing Ukrainian officials to publicly announce the Burisma investigation.

A clear contrast emerged between the two days of hearings. Hill and Holmes, career experts on Ukraine and Russia, quickly connected the dots. Sondland and Volker maintained that they didn't right away. Admitting that they knew it was all about the Bidens might risk giving away the game, and would weaken Trump's efforts to claim that this affair was about policy, not politics.

Democrats aren't buying it -- and neither was Hill. Asked about Sondland's denials, she said "it is not credible to me that he was oblivious" to the connection between Biden and Burisma.

Hill testified that Sondland was involved in a "domestic political errand," while she and others were trying to stay involved in "national security foreign policy." Democrats could use this testimony to argue that Trump used his office for personal gain, not to promote US policy. That could feature front and center in an article of impeachment on Trump's alleged abuse of power.

More confirmation of the quid pro quo

The witnesses Thursday confirmed -- for the umpteenth time -- there was a quid pro quo.

It wasn't a new revelation. One witness after another has testified that the Trump administration tried to use a White House invitation and US military assistance as leverage to pressure the new Ukrainian government into announcing investigations into Trump's political rivals.

"It became very clear that the White House meeting itself was being predicated on other issues," Hill said. "Namely investigations and the questions about the election interference in 2016."

Rep. Adam Schiff, the Democratic chairman, asked Holmes if Ukraine "felt the pressure" to launch the investigations that Trump was requesting. Holmes replied, "yes sir," and added, "although the hold on the security assistance may have been lifted, there were still things they wanted that they weren't getting, including a meeting with the president in the Oval Office."

This came on the heels of Sondland's bombshell-filled hearing on Wednesday morning, when he conceded for the first time, in stark and explicit terms, that there was a quid pro quo.

This testimony undercuts Trump's insistence that he wanted 'nothing" from Ukraine and that there was not a quid pro quo. Trump has continued making this case even as the evidence continues to pile up against him. (He tweeted "no quid pro quo" before Thursday's hearing.)

The pressure is rising on Bolton to testify

It looks like this phase of the impeachment inquiry -- public hearings at the House Intelligence Committee -- is drawing to a close. But the American public didn't hear from some key players.

That includes White House chief of staff Mick Mulvaney, who implemented Trump's order to freeze US military aid for Ukraine. It also includes former national security adviser John Bolton, who has firsthand knowledge of the Ukraine saga and compared the situation to a "drug deal."

"I believe that those who have information that the Congress deems relevant have a legal and a moral obligation to provide it," Hill said, in an implicit rebuke of Bolton, her onetime colleague.

Bolton was spotted on Thursday walking down Manhattan's Fifth Avenue during the hearings, not watching the early session where Hill described his concerns about the Ukraine schemes. He refused to cooperate with the inquiry, but he is writing a book that will come out next year.

CNN's Lauren Fox and Manu Raju contributed to this report.
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