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1. What is the definition of 'but that' or its synonym? --
But that = except that. It is more formal2. Is 'but that' an idiom?--
No, it's a 'complex subordinator' (i.e . is more than a single word) 3. Could you give me some examples of 'but that' in sentences? --
Nothing would satisfy her but that I cater to her every whim.