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Theorem orri 389
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 383 . 2 ((𝜑𝜓) ↔ (¬ 𝜑𝜓))
31, 2mpbir 219 1 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wo 381
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 195  df-or 383
This theorem is referenced by:  orci  403  olci  404  pm2.25  417  exmid  429  pm2.13  432  pm3.12  519  pm5.11  923  pm5.12  924  pm5.14  925  pm5.15  928  pm5.55  936  pm5.54  940  rb-ax2  1668  rb-ax3  1669  rb-ax4  1670  exmo  2482  axi12  2587  axbnd  2588  exmidne  2791  ifeqor  4081  fvbr0  6110  letrii  10013  numclwwlkdisj  26373  bj-curry  31518  poimirlem26  32401  tsim2  32904  tsbi3  32908  tsan2  32915  tsan3  32916  clsk1indlem2  37156  clwwlksndisj  41275
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