Theorem pm2.61d1 151

Description: Inference eliminating an antecedent. (Contributed by NM, 15-Jul-2005.)

Hypotheses

Ref	Expression
pm2.61d1.1	⊢ (φ → (ψ → χ))
pm2.61d1.2	⊢ (¬ ψ → χ)

Assertion

Ref	Expression
pm2.61d1	⊢ (φ → χ)

Proof of Theorem pm2.61d1

Step	Hyp	Ref	Expression
1		pm2.61d1.1	. 2 ⊢ (φ → (ψ → χ))
2		pm2.61d1.2	. . 3 ⊢ (¬ ψ → χ)
3	2	a1i 10	. 2 ⊢ (φ → (¬ ψ → χ))
4	1, 3	pm2.61d 150	1 ⊢ (φ → 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:  ja  153  pm2.61nii  158  pm2.01d  161  ax10lem2  1937  mo  2226  2mo  2282  mosubopt  4613  funfv  5376  fvmptnf  5724