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

Theorem orri 376
Description: Infer disjunction from implication. (Contributed by NM, 11-Jun-1994.)
Hypothesis
Ref Expression
orri.1  |-  ( -. 
ph  ->  ps )
Assertion
Ref Expression
orri  |-  ( ph  \/  ps )

Proof of Theorem orri
StepHypRef Expression
1 orri.1 . 2  |-  ( -. 
ph  ->  ps )
2 df-or 370 . 2  |-  ( (
ph  \/  ps )  <->  ( -.  ph  ->  ps )
)
31, 2mpbir 209 1  |-  ( ph  \/  ps )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 368
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 185  df-or 370
This theorem is referenced by:  orci  390  olci  391  pm2.25  404  exmid  415  pm2.13  418  pm3.12  500  pm5.11  884  pm5.12  885  pm5.14  886  pm5.15  889  pm5.55  897  pm5.54  902  rb-ax2  1573  rb-ax3  1574  rb-ax4  1575  exmo  2295  axi12  2419  axbnd  2420  exmidne  2648  abvor0  3789  ifeqor  3970  fvbr0  5877  letrii  9712  numclwwlkdisj  25056  tsim2  30513  tsbi3  30517  tsan2  30524  tsan3  30525
  Copyright terms: Public domain W3C validator