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Theorem orel1 644
Description: Elimination of disjunction by denial of a disjunct. Theorem *2.55 of [WhiteheadRussell] p. 107. (Contributed by NM, 12-Aug-1994.) (Proof shortened by Wolf Lammen, 21-Jul-2012.)
Assertion
Ref Expression
orel1 𝜑 → ((𝜑𝜓) → 𝜓))

Proof of Theorem orel1
StepHypRef Expression
1 pm2.53 641 . 2 ((𝜑𝜓) → (¬ 𝜑𝜓))
21com12 27 1 𝜑 → ((𝜑𝜓) → 𝜓))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wo 629
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 630
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  biorf  663  pm2.25dc  792  pm2.85dc  811  euor2  1958  prel12  3539  funun  4907  acexmidlema  5466  acexmidlemb  5467
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