Editing Proof by contradiction (section)

=== Law of non-contradiction ===

The [[law of noncontradiction]] was first stated as a metaphysical principle by [[Aristotle]]. It posits that a proposition and its negation cannot both be true, or equivalently, that a proposition cannot be both true and false. Formally the law of non-contradiction is written as ''¬(P ∧ ¬P)'' and read as "it is not the case that a proposition is both true and false". The law of non-contradiction neither follows nor is implied by the principle of Proof by contradiction.

The laws of excluded middle and non-contradiction together mean that exactly one of ''P'' and ''¬P'' is true.