On the table are two similar technical definitions of what that promise means: one proposed by the government, and one proposed by a pro-EU member of May's Conservative Party, Dominic Grieve.
Mrs May opposed the move on the grounds that it would tie her hands in Brexit negotiations.
What the Tory rebels wanted was assurance that, if the final negotiations fall apart and the government walks away with no deal, MPs would then be given a vote on what we do next.
Peers accepted the amendment to the EU (Withdrawal) Bill sent to them from the House of Commons, meaning the bill now goes for Royal Assent, becoming law.
"We won't be accepting the Lords amendment", the source said, referring to a decision in the upper house of parliament on Monday to again try to force the government to hand the House of Commons more control over Britain's exit from the EU.
LAFC's Marco Ureña on Costa Rica facing Brazil: "They're not invincible"
Neymar is a very skilled player and it's true that people have tried to stop him a little aggressively. "They're not invincible. The Paris St Germain forward appeared for training but spent a few minutes grimacing before retiring to the dressing room.
The government's Brexit bill has passed through Parliament after Theresa May saw off a revolt by Tory MPs.
There were other MPs who were happy with the result too.
Mr Davis's statement also mentioned MPs being able to table their own motions and have votes on them.
Bradford West's Naz Shah, who has been ill, was pushed in to vote in a wheelchair with a sick bucket on her lap, in scenes which fellow Labour MP Catherine McKinnell said showed an "utter lack of humanity and compassion" from the Government.
But Downing Street left no doubt ministers are confident of drafting a motion which Mr Bercow will deem to be unamendable.
Potential Tory rebels were bristling at Theresa May's plan to offer only a symbolic vote on an unamendable "neutral motion" which would simply note that no agreement has been reached with Brussels.
Iceland Captain, Gunnarsson: Nigeria Will Be Tougher Than Argentina
The Leicester City striker struck twice in the second half to keep the Super Eagles in with a chance of reaching the last-16. Nigeria coach Gernot Rohr said he is not under pressure ahead of the match.
Meanwhile pregnant Liberal Democrat deputy leader Jo Swinson and Labour MP Laura Pidcock turned out to oppose the PM's plans despite being close to their due dates.
- If that deal is rejected by parliament, or if the government decides no deal is possible, or if a deal has not been reached by January 21, 2019, the government has to come up with a new plan of action and present it to parliament.
Mr Grieve and his pro-EU chums believe this was an "obvious acknowledgement" of the sovereignty of Parliament over the Executive "in black and white language".
Sterling rose to a session high against the euro and climbed against the dollar after May won the rare victory, one which will give the weakened prime minister a firmer footing when she travels to Brussels next week for an European Union summit.
Leading Brexiteer Jacob Rees-Mogg said the vote would strengthen Mrs May's hand at a summit of European Union leaders in Brussels on June 28-29.
Mosquito infected with West Nile Virus collected in Dauphin County
Unfortunately, with the added temperature spike comes the increase of West Nile Virus (WNV ) vectors, most notably mosquitoes. Wear a long sleeve shirt, long trousers , and a hat when going into mosquito-infested areas, such as wetlands or wooded areas.