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Mr Corbyn has ordered Labour MPs to back the Brexit Bill to make way for Mrs May to trigger the exit
The Labour leader is imposing a three-line whip on his MPs in a move which risks the resignation of high-profile shadow cabinet ministers like Clive Lewis.
The move to vote for the European Union (Notification of Withdrawal) Bill at third reading, its final Commons stage, was agreed by the shadow cabinet on Tuesday morning, the source said.
The issue caused heated debate at a meeting of the Parliamentary Labour Party (PLP) on Monday after 47 MPs defied Mr Corbyn and voted against the Bill at its first Commons stage last week.
It is believed the party's chief whip Nick Brown wanted "consistency" in dealing with the passage of the Bill, which Labour is currently trying to amend at committee stage.
The Labour leader is imposing a three-line whip on his MPs
The imposition of a three-line whip before knowing if safeguards demanded by Labour are successfully added to the Bill risks forcing the resignation of Mr Lewis.
The shadow business secretary has vowed to oppose the Bill unless Labour amendments, including a move to ensure a "meaningful" parliamentary vote on the final exit deal the Prime Minister achieves, are passed in the Commons.
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Continued cooperation with the EU to tackle terrorism and international crime.
Diane Abbott did not vote on the Bill after a migraine forced her to leave Parliament early
Remain-backing Tory MPs have indicated they could be willing to support amendments seeking to ensure Parliament gets a say on the "endgame" if Brexit negotiations collapse without a deal.
But Mr Corbyn's order also appears to put pressure on his close ally and shadow home secretary Diane Abbott, who did not vote on the Bill last week after a migraine forced her to leave Parliament early.
Critics have accused Ms Abbott of falling victim to "Brexit flu" because her constituency voted overwhelmingly in the referendum to Remain.