Theorem pm2.21d 98

Description: A contradiction implies anything. Deduction from pm2.21 100. (Contributed by NM, 10-Feb-1996.)

Hypothesis

Ref	Expression
pm2.21d.1	⊢ (φ → ¬ ψ)

Assertion

Ref	Expression
pm2.21d	⊢ (φ → (ψ → χ))

Proof of Theorem pm2.21d

Step	Hyp	Ref	Expression
1		pm2.21d.1	. . 3 ⊢ (φ → ¬ ψ)
2	1	a1d 22	. 2 ⊢ (φ → (¬ χ → ¬ ψ))
3	2	con4d 97	1 ⊢ (φ → (ψ → 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:  pm2.21dd  99  pm2.21  100  2falsed  340  pm5.14  856  ecase2d  906  prlem1  928  sbc2or  3054  eq0rdv  3585  rzal  3651  ssofss  4076  tfinltfin  4501  clos1nrel  5886  nchoicelem12  6300