Theorem pm2.61d 150

Description: Deduction eliminating an antecedent. (Contributed by NM, 27-Apr-1994.) (Proof shortened by Wolf Lammen, 12-Sep-2013.)

Hypotheses

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

Assertion

Ref	Expression
pm2.61d	⊢ (φ → χ)

Proof of Theorem pm2.61d

Step	Hyp	Ref	Expression
1		pm2.61d.2	. . . 4 ⊢ (φ → (¬ ψ → χ))
2	1	con1d 116	. . 3 ⊢ (φ → (¬ χ → ψ))
3		pm2.61d.1	. . 3 ⊢ (φ → (ψ → χ))
4	2, 3	syld 40	. 2 ⊢ (φ → (¬ χ → χ))
5	4	pm2.18d 103	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:  pm2.61d1  151  pm2.61d2  152  pm5.21ndd  343  bija  344  pm2.61dan  766  ecase3d  909  nfsb4t  2080  pm2.61dne  2594