Theorem pm2.61nii 186

Description: Inference eliminating two antecedents. (Contributed by NM, 13-Jul-2005.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof shortened by Wolf Lammen, 13-Nov-2012.)

Hypotheses

Ref	Expression
pm2.61nii.1	⊢ (𝜑 → (𝜓 → 𝜒))
pm2.61nii.2	⊢ (¬ 𝜑 → 𝜒)
pm2.61nii.3	⊢ (¬ 𝜓 → 𝜒)

Assertion

Ref	Expression
pm2.61nii	⊢ 𝜒

Proof of Theorem pm2.61nii

Step	Hyp	Ref	Expression
1		pm2.61nii.1	. . 3 ⊢ (𝜑 → (𝜓 → 𝜒))
2		pm2.61nii.3	. . 3 ⊢ (¬ 𝜓 → 𝜒)
3	1, 2	pm2.61d1 182	. 2 ⊢ (𝜑 → 𝜒)
4		pm2.61nii.2	. 2 ⊢ (¬ 𝜑 → 𝜒)
5	3, 4	pm2.61i 184	1 ⊢ 𝜒

Syntax hints:  ¬ wn 3   → wi 4

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

This theorem is referenced by:  ecase  1028  3ecase  1468  prex  5323  nbgr0vtxlem  27129