President Trump is unlikely to face prosecution relating to the Russia investigation after he leaves office, even though current Justice Department policy allows it, according to Neil Quinter.

Bringing obstruction of justice charges against Trump post-term would not be in keeping with custom, the former counsel for Sen. Dianne Feinstein, D-Calif., claimed Thursday on "The Daily Briefing."

"I don't think there's going to be a real appetite after an election for going after someone criminally," he said.

"That's kind of a third-world approach and not really keeping with American tradition."

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Quinter was responding to an exchange between Rep. Kenneth Buck, R-Colo., and former Special Counsel Robert Mueller during Wednesday's House Judiciary Committee hearing.

In the hearing, Buck asked whether the president could be prosecuted after leaving office -- since Office of Legal Counsel opinion says he cannot be indicted while in the White House.

"Yes," Mueller responded. Buck asked the question again to confirm Mueller's view. The former special counsel offered the same answer.

In the interview with Julie Banderas, Quinter said Mueller was offering, "standard Justice Department dogma."

In regard to other potential proceedings, Banderas said Democrats are, "keeping impeachment on the table."

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Earlier Thursday, Rep. Lori Trahan, D-Mass., became the first lawmaker to come out in favor of impeachment since Mueller's hearing.

Trahan recalled her work as a House Democratic aide during the Clinton impeachment.

"I know how disruptive it will be to the country," she told Fox News in Washington. "But, at the end of the day for me, no president -- not his one, not the next one -- is above the law. That's why I came up for impeachment proceedings."

Fox News' Chad Pergram contributed to this report.