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Theorem orri 862
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 848 . 2 ((𝜑𝜓) ↔ (¬ 𝜑𝜓))
31, 2mpbir 231 1 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wo 847
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 848
This theorem is referenced by:  orci  865  olci  866  pm2.25  889  curryax  893  exmid  894  pm2.13  897  pm5.11g  945  pm5.12  947  pm5.14  948  pm5.55  950  pm3.12  995  pm5.15  1014  pm5.54  1019  4exmid  1051  rb-ax2  1749  rb-ax3  1750  rb-ax4  1751  exmo  2539  axi12  2703  exmidne  2947  ifeqor  4581  fvbr0  6935  letrii  11383  clwwlknondisj  30139  poimirlem26  37632  tsbi3  38121  tsan2  38128  tsan3  38129  clsk1indlem2  44031
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