Theorem con4d 97

Description: Deduction derived from Axiom ax-3 8. (Contributed by NM, 26-Mar-1995.)

Hypothesis

Ref	Expression
con4d.1	⊢ (φ → (¬ ψ → ¬ χ))

Assertion

Ref	Expression
con4d	⊢ (φ → (χ → ψ))

Proof of Theorem con4d

Step	Hyp	Ref	Expression
1		con4d.1	. 2 ⊢ (φ → (¬ ψ → ¬ χ))
2		ax-3 8	. 2 ⊢ ((¬ ψ → ¬ χ) → (χ → ψ))
3	1, 2	syl 15	1 ⊢ (φ → (χ → ψ))

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:  pm2.21d  98  pm2.18  102  con2d  107  con1d  116  mt4d  130  impcon4bid  196  con4bid  284  exim  1575  sp  1747  spOLD  1748  axi11e  2332  necon2ad  2565  spc2gv  2943  spc3gv  2945  addceq0  6220