Theorem pm2.24ii 124

Description: A contradiction implies anything. Inference from pm2.24 101. (Contributed by NM, 27-Feb-2008.)

Hypotheses

Ref	Expression
pm2.24ii.1	⊢ φ
pm2.24ii.2	⊢ ¬ φ

Assertion

Ref	Expression
pm2.24ii	⊢ ψ

Proof of Theorem pm2.24ii

Step	Hyp	Ref	Expression
1		pm2.24ii.1	. 2 ⊢ φ
2		pm2.24ii.2	. . 3 ⊢ ¬ φ
3	2	pm2.21i 123	. 2 ⊢ (φ → ψ)
4	1, 3	ax-mp 5	1 ⊢ ψ

Syntax hints:  ¬ wn 3

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is referenced by: (None)