Proof by contradiction
Formalization

The principle may be formally expressed as the propositional formula ¬¬P ⇒ P, equivalently (¬P ⇒ ⊥) ⇒ P, which reads: "If assuming P to be false implies falsehood, then P is true."

In natural deduction the principle takes the form of the rule of inference

which reads: "If ¬ ¬ P {\displaystyle \lnot \lnot P} is proved, then P {\displaystyle P} may be concluded."

In sequent calculus the principle is expressed by the sequent

which reads: "Hypotheses Γ {\displaystyle \Gamma } and ¬ ¬ P {\displaystyle \lnot \lnot P} entail the conclusion P {\displaystyle P} or Δ {\displaystyle \Delta }."
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