pm2.24ii - Intuitionistic Logic Explorer

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Theorem pm2.24ii 637

Description: A contradiction implies anything. Inference from pm2.24 611. (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 636	. 2 ⊢ (𝜑 → 𝜓)
4	1, 3	ax-mp 5	1 ⊢ 𝜓

Colors of variables: wff set class

Syntax hints: ¬ wn 3

This theorem was proved from axioms: ax-mp 5 ax-in2 605

This theorem is referenced by: (None)