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Theorem con4d 97
Description: Deduction derived from axiom ax-3 7. (Contributed by NM, 26-Mar-1995.)
Hypothesis
Ref Expression
con4d.1 (φ → (¬ ψ → ¬ χ))
Assertion
Ref Expression
con4d (φ → (χψ))

Proof of Theorem con4d
StepHypRef Expression
1 con4d.1 . 2 (φ → (¬ ψ → ¬ χ))
2 ax-3 7 . 2 ((¬ ψ → ¬ χ) → (χψ))
31, 2syl 15 1 (φ → (χψ))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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  2564  spc2gv  2942  spc3gv  2944  addceq0  6219
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