It was far more serious than that. Blair didn't just change the direction of the Labour party as Fingers said. He created a whole new political position to the right of centre, pretending it was still Labour. Keir Hardie, Clement Attlee, Michael Foot, James Callaghan, John Smith etc would have never have accepted that as Labour, just as Corbyn always refused to.
There are two relevant precedents:
Hugh Gaitskill as Labour leader repeatedly attempted to go in Blair's direction but the party refused to allow that, seeing that it would no longer be Labour.
The other precedent being that the Lib Dems are not the original Liberal party, even though they have Liberal policies. That's because they were an evolution of the Social Democrats formed by the Labour "Gang of Four" who broke away from the Labour party to do that. Later they merged with the failing Liberal party with varying names before finally now named the LibDems.
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