Theorem pm2.61d2 152

Description: Inference eliminating an antecedent. (Contributed by NM, 18-Aug-1993.)

Hypotheses

Ref	Expression
pm2.61d2.1	⊢ (φ → (¬ ψ → χ))
pm2.61d2.2	⊢ (ψ → χ)

Assertion

Ref	Expression
pm2.61d2	⊢ (φ → χ)

Proof of Theorem pm2.61d2

Step	Hyp	Ref	Expression
1		pm2.61d2.2	. . 3 ⊢ (ψ → χ)
2	1	a1i 10	. 2 ⊢ (φ → (ψ → χ))
3		pm2.61d2.1	. 2 ⊢ (φ → (¬ ψ → χ))
4	2, 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:  pm2.61ii  157  jaoi  368  dvelimv  1939  nfald2  1972  nfsb4t  2080  nfsbd  2111  nfabd2  2508  dff3  5421