1.NounA 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."