This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem pm2.21

Description: From a wff and its negation, anything follows. Theorem *2.21 of WhiteheadRussell p. 104. Also called the Duns Scotus law. Its commuted form is pm2.24 and its associated inference is pm2.21i . (Contributed by NM, 29-Dec-1992) (Proof shortened by Wolf Lammen, 14-Sep-2012)

		Ref	Expression
	Assertion	pm2.21	⊢ ( ¬ 𝜑 → ( 𝜑 → 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		id	⊢ ( ¬ 𝜑 → ¬ 𝜑 )
2	1	pm2.21d	⊢ ( ¬ 𝜑 → ( 𝜑 → 𝜓 ) )