Washington (CNN) The top US diplomat in Ukraine, Bill Taylor, testified behind closed doors Tuesday as part of the ongoing impeachment inquiry led by House Democrats. In his opening statement, Taylor gave an account of his concern, beginning in August of this year, that the US relationship with Ukraine "was being fundamentally undermined by an irregular, informal channel of U.S. policy-making" led by President Donald Trump's personal attorney, Rudy Giuliani.

In the 15-page statement obtained by CNN, Taylor corroborated many of the claims made by the intelligence community's whistleblower, whose complaint and subsequent inspector general's report prompted the impeachment inquiry.

Taylor also provided witness testimony to the events around the temporary withholding of US military aid to Ukraine, the July 25 phone call between Trump and Ukrainian President Volodymyr Zelensky, and the eventual release of that military aid in anticipation of a face-to-face meeting between the two leaders.

Taylor also undercut a key assertion made by US Ambassador to the European Union Gordon Sondland, who testified to Congress last week that Trump had not directed him to tell the Zelensky government that a Ukrainian investigation into Trump's political opponents, including former vice president Joe Biden, was a precondition for having the meeting with Trump.

On Tuesday, three lawmakers who took part in Taylor's closed interview on Capitol Hill told CNN that Taylor's testimony was inconsistent with what they heard last week from Sondland. One of them, Democratic Rep. Gerry Connolly, said that Sondland "may very well have to come back. He's got some explaining to do."

Here's a breakdown of 5 of the most important lines from Taylor's statement.

Giuliani's Irregular channel

Taylor: "...there was an irregular, informal channel of U.S. policy-making with respect to Ukraine, one which included then-Special Envoy Kurt Volker, Ambassador Sondland, Secretary of Energy Rick Perry, and as I subsequently learned, Mr. Giuliani."

Context: Taylor laid out, naming names, the players involved with Giuliani in the Trump attorney's rogue operation to get the President to push Ukraine to pursue investigations into his political opponents.

Giuliani's role in shaping US policy toward Ukraine, as a part of this informal channel, was mentioned in the whistleblower's complaint. The whistleblower described other US officials being "deeply concerned by what they viewed as Mr. Giuliani's circumvention of national security decisionmaking processes to engage with Ukrainian officials and relay messages back and forth between Kyiv and the President."

'Leave no stone unturned'

Taylor: "Ambassador Sondland told me that he had recommended to President Zelenskyy that he use the phrase, 'I will leave no stone unturned' with regard to 'investigations' when President Zelenskyy spoke with President Trump."

Context: This is the first instance of Taylor witnessing a member of the irregular channel to Ukraine pushing the Ukrainians to help Trump pursue his domestic political agenda. The "investigations" came to be understood by Taylor and by others who have testified before Congress to mean a pursuit into two opponents of Trump: Biden and his connection with Ukrainian energy company Burisma; and the supposed collusion by Ukrainians and Democrats during the 2016 election.

This conversation between Sondland and Taylor happened on July 20, five days before the July 25 call between Trump and Zelensky in which the American President mentioned both cases and encouraged Zelensky to talk to both Giuliani and Attorney General Bill Barr. That phone call prompted the whistleblower's complaint.

Allegation of a quid pro quo

Taylor: "...Ambassador Sondland told me that President Trump had told him that he wants President Zelenskyy to state publicly that Ukraine will investigate Burisma and alleged Ukrainian interference in the 2016 U.S. election."

Context: The ongoing hold on military aid to Ukraine had vexed Taylor for weeks as nobody in the administration offered a clear explanation for why it had not sent the money. Taylor testified that on September 1 he learned from National Security Council aide Tim Morrison that Sondland had spoken with a top Zelensky adviser, Andriy Yermak, in Warsaw, where Zelensky and Vice President Mike Pence were meeting. Morrison told Taylor that Sondland had informed Yermak that the funding would not come until Zelensky "committed to pursue the Burisma investigation."

Taylor described being "alarmed" at hearing for the first time the link between the military aid and the investigation of Biden. He texted Sondland that same day to express his concern about this outlining of a quid pro quo, prompting Sondland to ask Taylor to call him. Taylor said that phone call is when Sondland told him Trump had requested the quid pro quo.

Those text messages were released as part of Volker's testimony to Congress earlier this month. In his testimony, Sondland claimed withholding aid in this way -- to influence an American election -- would be wrong. "I did not and would not ever participate in such undertakings," Sondland testified. But on Tuesday Taylor testified that Sondland had participated in exactly that.

Promise to investigate Biden

Taylor: "...President Trump did insist that President Zelenskyy go to a microphone and say he is opening investigations of Biden and 2016 election interference, and that President Zelenskyy should want to do this himself."

Context: This is further evidence from Taylor that Trump intended for the military aid to be withheld unless Zelensky complied with Trump's demand to act in a way that benefited Trump politically. The September 7 conversation between Sondland and Trump that Taylor is recounting here comes more than a week after the hold on the money was made public in an August 29 Politico report and after a meeting Taylor had with Zelensky in which the Ukrainian President was pressing for answers about the issue.

Taylor went on to recount a conversation he had with Sondland on September 8 in which Sondland described Trump as being "adamant" that Zelensky "clear things up" about pursuing these investigations or risk a "stalemate." Taylor says he perceived the stalemate as meaning Ukraine would not receive the aid.

Foreign policy undercut

Taylor: "...the push to make President Zelenskyy publicly commit to investigations of Burisma and alleged interference in the 2016 election showed how the official foreign policy of the United States was undercut by the irregular efforts led by Mr. Giuliani."

Context: This statement from Taylor encapsulates his perception of the divide between the official foreign policy arm of the US government and the efforts by Giuliani, and how that divide was being perceived by Ukraine.

For a quid pro quo threat to be effective, the Ukrainians would have had to discount what Taylor describes as a bipartisan effort by him and other US officials to reassure Zelensky that the US policy toward Ukraine remained unchanged. To Taylor, the counter-narrative from Giuliani undermined the authority of officials like himself by appearing to condition that policy on cooperation with Trump's own domestic political concerns.

That goes to the heart of the concern that House Democrats have, and explains why Taylor on September 9 wrote his now infamous text to Sondland, "I think it's crazy to withhold security assistance for help with a political campaign."