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Theorem orri 863
Description: Infer disjunction from implication. (Contributed by NM, 11-Jun-1994.)
Hypothesis
Ref Expression
orri.1 𝜑𝜓)
Assertion
Ref Expression
orri (𝜑𝜓)

Proof of Theorem orri
StepHypRef Expression
1 orri.1 . 2 𝜑𝜓)
2 df-or 849 . 2 ((𝜑𝜓) ↔ (¬ 𝜑𝜓))
31, 2mpbir 231 1 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wo 848
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 207  df-or 849
This theorem is referenced by:  orci  866  olci  867  pm2.25  890  curryax  894  exmid  895  pm2.13  898  pm5.11g  946  pm5.12  948  pm5.14  949  pm5.55  951  pm3.12  996  pm5.15  1015  pm5.54  1020  4exmid  1052  rb-ax2  1753  rb-ax3  1754  rb-ax4  1755  exmo  2542  axi12  2706  exmidne  2950  ifeqor  4577  fvbr0  6935  letrii  11386  clwwlknondisj  30130  poimirlem26  37653  tsbi3  38142  tsan2  38149  tsan3  38150  clsk1indlem2  44055
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