Theorem pm2.61nii 158

Description: Inference eliminating two antecedents. (Contributed by NM, 5-Aug-1993.) (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 151	. 2 ⊢ (φ → χ)
4		pm2.61nii.2	. 2 ⊢ (¬ φ → χ)
5	3, 4	pm2.61i 156	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  908  3ecase  1286