The leaders have not wasted time wondering what motivated the Prime Minister's offer, or why he went to the trouble and expense of a referendum if he did not mean to act on it. They simply resolved not to trust him. The deal they have made with him has to be endorsed by Greece's Parliament this week if it is to take effect when the debt is due on Monday.
As German Chancellor Angela Merkel said, trust in Greece "needs to be rebuilt".
A majority of the Parliament looks likely to accept the terms of the bailout, though not a majority of Mr Tsipras' party. His own future looks doubtful. A new government might emerge after the vote tomorrow or new elections might be called.
But whatever happens, the eurozone looks stronger now. Greek voters have had a salutary experience. Six months ago they elected a Government that thought it could default on some debt, demand easier credit conditions and keep the euro.
It was a game of bluff and Greece has blinked. To keep the currency it will be governed as euro partners demand, like Ireland and Portugal before it. Each crisis in the common currency is working out well for European unity.