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	$$⊢\left(\phi \to \neg \phi \right)\to \neg \phi$$

Proof

Step	Hyp	Ref	Expression
1		id	$$⊢\neg \phi \to \neg \phi$$
2	1 1	ja	$$⊢\left(\phi \to \neg \phi \right)\to \neg \phi$$