 In classical logic, particularly in propositional and first-order logic, a proposition formula_1 is a contradiction if and only if formula_2.Since for contradictory formula_1 it is true that formula_4 for all formula_5 (because formula_6), one may prove any proposition from a set of axioms which contains contradictions.This is called the "principle of explosion" or "ex falso quodlibet" ("from falsity, anything follows").