Consequentia mirabilis

Consequentia mirabilis is the classical logical principle that if a proposition follows from its own negation, then the proposition is true.

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Classical logic: A family of logical systems that accept principles such as excluded middle and double negation elimination. Consequentia mirabilis is valid in classical logic because that system permits reasoning by contradiction.
Medieval logic: The study and development of logic in Europe and the Islamic world during the Middle Ages. The Latin name is associated with the medieval logical tradition in which the principle circulated.
Proposition: A declarative content that can be assigned a truth value in a logical system. The principle applies to a proposition and its negation, not directly to every sentence or argument.
Modus tollens: An inference rule that derives not-P from if P then Q and not-Q. It reverses the conditional direction used in the principle's familiar formulation.
Proof by contradiction: A proof method that establishes a claim by deriving a contradiction from its negation. The principle can be derived by assuming the proposition false and using its consequence to reach a contradiction.
Aristotle: An ancient Greek philosopher whose works shaped formal logic and many later philosophical traditions. Aristotelian treatments of proof by impossibility provide an ancient background for the principle's reasoning pattern.
Negation: A logical operation that forms a statement denying the truth of a proposition. The principle begins with the proposition's negation as its antecedent.
Ex falso quodlibet: The classical inference that a contradiction entails any proposition. This rule starts from contradiction, whereas consequentia mirabilis obtains a proposition from its negation as a premise.
Law of excluded middle: The classical principle that every proposition is true or false: P or not P. Excluded middle supplies the two cases behind a standard derivation of the principle.
Reductio ad absurdum: An argument that derives an absurdity or contradiction from an assumption to reject that assumption. Consequentia mirabilis is a compact form of reasoning by reduction to contradiction.