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- (logic) A proof showing that if an assumption A is true then a consequent statement or conclusion B must also be true, i.e. B is true on the condition that A is true.
- A conditional proof corresponds to the application of what Douglas Hofstadter calls the "Fantasy Rule" in his masterwork "GEB:EGB". Surprisingly, the theory of propositional calculus which he develops in GEB:EGB employs several inference rules but no axioms: the need for any axioms is done away with through application of the Fantasy Rule.