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Theorem orel2 644
Description: Elimination of disjunction by denial of a disjunct. Theorem *2.56 of [WhiteheadRussell] p. 107. (Contributed by NM, 12-Aug-1994.) (Proof shortened by Wolf Lammen, 5-Apr-2013.)
Assertion
Ref Expression
orel2 φ → ((ψ φ) → ψ))

Proof of Theorem orel2
StepHypRef Expression
1 idd 21 . 2 φ → (ψψ))
2 pm2.21 547 . 2 φ → (φψ))
31, 2jaod 636 1 φ → ((ψ φ) → ψ))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   wo 628
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 545  ax-io 629
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  biorfi  664  pm2.64  713  pm5.71dc  867  ecased  1238  19.30dc  1515  dveeq2  1693  prel12  3533  funun  4887
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