Metamath Proof Explorer

Theorem pm2.01

Description: Weak Clavius law. If a formula implies its negation, then it is false. A form of "reductio ad absurdum", which can be used in proofs by contradiction. Theorem *2.01 of WhiteheadRussell p. 100. Provable in minimal calculus, contrary to the Clavius law pm2.18 . (Contributed by NM, 18-Aug-1993) (Proof shortened by Mel L. O'Cat, 21-Nov-2008) (Proof shortened by Wolf Lammen, 31-Oct-2012)

Ref Expression
Assertion pm2.01 φ ¬ φ ¬ φ


Step Hyp Ref Expression
1 id ¬ φ ¬ φ
2 1 1 ja φ ¬ φ ¬ φ