Principle of Explosion

A rule of classical logic (ex falso quodlibet) stating that once a contradiction is admitted in a deductive system (both P and ¬P), any proposition can be validly inferred from it.

The inference principle, ex contradictione quodlibet, that once a contradiction (both P and ¬P) is present in a deductive system, any proposition Q can be derived; contradictions lead to logical triviality in classical consequence relations.

A logical principle of classical consequence relations stating that once a contradiction (both P and ¬P) is admitted, any proposition Q can be validly inferred; the presence of a contradiction renders the consequence relation explosive (trivializes the theory by making every formula derivable).