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Theorem ord 366
Description: Deduce implication from disjunction. (Contributed by NM, 18-May-1994.)
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 df-or 359 . 2 ((ψ χ) ↔ (¬ ψχ))
31, 2sylib 188 1 (φ → (¬ ψχ))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4   wo 357
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-or 359
This theorem is referenced by:  orcanai  879  oplem1  930  ecase23d  1285  19.33b  1608  eqsn  3867  nnsucelr  4428  lenltfin  4469  vfin1cltv  4547  phi011lem1  4598  foconst  5280  nceleq  6149  addceq0  6219  ncslemuc  6255  nchoicelem8  6296
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