MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  orri Structured version   Visualization version   GIF version

Theorem orri 390
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 384 . 2 ((𝜑𝜓) ↔ (¬ 𝜑𝜓))
31, 2mpbir 221 1 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wo 382
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 197  df-or 384
This theorem is referenced by:  orci  404  olci  405  pm2.25  418  exmid  430  pm2.13  433  pm3.12  520  pm5.11  946  pm5.12  947  pm5.14  948  pm5.15  951  pm5.55  957  pm5.54  963  4exmid  1021  rb-ax2  1718  rb-ax3  1719  rb-ax4  1720  exmo  2523  axi12  2629  axbnd  2630  exmidne  2833  ifeqor  4165  fvbr0  6253  letrii  10200  clwwlknondisj  27086  clwwlknondisjOLD  27090  bj-curry  32667  poimirlem26  33565  tsim2  34068  tsbi3  34072  tsan2  34079  tsan3  34080  clsk1indlem2  38657
  Copyright terms: Public domain W3C validator