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Theorem orri 861
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 847 . 2 ((𝜑𝜓) ↔ (¬ 𝜑𝜓))
31, 2mpbir 230 1 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wo 846
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 206  df-or 847
This theorem is referenced by:  orci  864  olci  865  pm2.25  889  curryax  893  exmid  894  pm2.13  897  pm5.11g  943  pm5.12  945  pm5.14  946  pm5.55  948  pm3.12  993  pm5.15  1012  pm5.54  1017  4exmid  1051  rb-ax2  1756  rb-ax3  1757  rb-ax4  1758  exmo  2537  axi12  2702  exmidne  2951  ifeqor  4580  fvbr0  6921  letrii  11339  clwwlknondisj  29364  poimirlem26  36514  tsbi3  37003  tsan2  37010  tsan3  37011  clsk1indlem2  42793
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