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Theorem orel1 677
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 pm2.53 674 . 2 ((𝜑𝜓) → (¬ 𝜑𝜓))
21com12 30 1 𝜑 → ((𝜑𝜓) → 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:  biorf  696  pm2.25dc  826  pm2.85dc  845  euor2  2001  prel12  3589  funun  5009  acexmidlema  5580  acexmidlemb  5581
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