Metamath Proof Explorer

Theorem pm2.18

Description: Clavius law, or "consequentia mirabilis" ("admirable consequence"). If a formula is implied by its negation, then it is true. Can be used in proofs by contradiction. Theorem *2.18 of WhiteheadRussell p. 103. See also the weak Clavius law pm2.01 . (Contributed by NM, 29-Dec-1992) (Proof shortened by Wolf Lammen, 17-Nov-2023)

Ref Expression
Assertion pm2.18 ¬ φ φ φ


Step Hyp Ref Expression
1 id ¬ φ φ ¬ φ φ
2 1 pm2.18d ¬ φ φ φ