The Law of Non-Contradiction is a law in logic which states that for any sentence or proposition, it and its negation are not both true. In other words, the law states that there are no true contradictions.

The Law of Non-Contradiction is often stated as the axiom: ¬(φ ∧ ¬φ).

The Law of Non-Contradiction is also important to reductio ad absurdum as a rule of inference in proofs and argument forms. This rule uses contradictions to proclaim that some earlier assumption is absurd, but if contradictions are not counted as absurdities, then the assumptions that generate them cannot be rejected so easily.

Some non-classical logics reject the Law of Non-Contradiction and allow some sentences to be both true and false.