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Theorem ord 630
Description: Deduce implication from disjunction. (Contributed by NM, 18-May-1994.) (Revised by Mario Carneiro, 31-Jan-2015.)
Hypothesis
Ref Expression
ord.1 (φ → (ψ χ))
Assertion
Ref Expression
ord (φ → (¬ ψχ))

Proof of Theorem ord
StepHypRef Expression
1 ord.1 . 2 (φ → (ψ χ))
2 pm2.53 628 . 2 ((ψ χ) → (¬ ψχ))
31, 2syl 14 1 (φ → (¬ ψχ))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   wo 616
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in2 533  ax-io 617
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  pm2.8  711  orcanai  825  ax-12  1384  swopo  3996  suc11g  4189  ordsoexmid  4194  nnsuc  4234  sotri2  4616
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