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Theorem orri 860
 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 846 . 2 ((𝜑𝜓) ↔ (¬ 𝜑𝜓))
31, 2mpbir 234 1 (𝜑𝜓)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 845 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 210  df-or 846 This theorem is referenced by:  orci  863  olci  864  pm2.25  888  curryax  892  exmid  893  pm2.13  896  pm5.11g  942  pm5.12  944  pm5.14  945  pm5.55  947  pm3.12  992  pm5.15  1011  pm5.54  1016  4exmid  1048  rb-ax2  1756  rb-ax3  1757  rb-ax4  1758  exmo  2560  axi12  2728  exmidne  2959  ifeqor  4464  fvbr0  6678  letrii  10788  clwwlknondisj  27980  poimirlem26  35348  tsbi3  35838  tsan2  35845  tsan3  35846  clsk1indlem2  41103
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