Theorem pm2.61ii 157

Description: Inference eliminating two antecedents. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Josh Purinton, 29-Dec-2000.)

Hypotheses

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

Assertion

Ref	Expression
pm2.61ii	⊢ χ

Proof of Theorem pm2.61ii

Step	Hyp	Ref	Expression
1		pm2.61ii.2	. 2 ⊢ (φ → χ)
2		pm2.61ii.1	. . 3 ⊢ (¬ φ → (¬ ψ → χ))
3		pm2.61ii.3	. . 3 ⊢ (ψ → χ)
4	2, 3	pm2.61d2 152	. 2 ⊢ (¬ φ → χ)
5	1, 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:  pm2.61iii  159  hbae  1953  sbequi  2059  sbcom  2089  sbcom2  2114  hbae-o  2153  hbequid  2160  ax17eq  2183  ax17el  2189