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Theorem orel2 726
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 pm2.21 617 . 2 𝜑 → (𝜑𝜓))
31, 2jaod 717 1 𝜑 → ((𝜓𝜑) → 𝜓))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wo 708
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in2 615  ax-io 709
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  biorfi  746  pm2.64  801  stdcn  847  pm5.71dc  961  ecased  1349  19.30dc  1625  dveeq2  1813  prel12  3767  funun  5252
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