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Theorem orel2 678
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 → ((𝜓𝜑) → 𝜓))

Proof of Theorem orel2
StepHypRef Expression
1 idd 21 . 2 𝜑 → (𝜓𝜓))
2 pm2.21 580 . 2 𝜑 → (𝜑𝜓))
31, 2jaod 670 1 𝜑 → ((𝜓𝜑) → 𝜓))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wo 662
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in2 578  ax-io 663
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  biorfi  698  pm2.64  748  pm5.71dc  903  ecased  1281  19.30dc  1559  dveeq2  1738  prel12  3583  funun  4994
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