Theorem pm2.24ii 121

Description: A contradiction implies anything. Inference associated with pm2.21i 120 and pm2.24i 151. (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 120	. 2 ⊢ (𝜑 → 𝜓)
4	1, 3	ax-mp 5	1 ⊢ 𝜓

This proof depends on syntax axioms:  ¬ wn 3

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-3 8

This theorem is used by:  dtrucor2  5348  bj-babygodel  37237  bj-dtrucor2v  37493  quantgodel  47629  quantgodelALT  47630  dtrucor3  49618