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 220 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 196  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  924  pm5.12  925  pm5.14  926  pm5.15  929  pm5.55  937  pm5.54  941  rb-ax2  1669  rb-ax3  1670  rb-ax4  1671  exmo  2483  axi12  2588  axbnd  2589  exmidne  2792  ifeqor  4082  fvbr0  6125  letrii  10041  numclwwlkdisj  26607  bj-curry  31712  poimirlem26  32605  tsim2  33108  tsbi3  33112  tsan2  33119  tsan3  33120  clsk1indlem2  37360  clwwlksndisj  41280
 Copyright terms: Public domain W3C validator