MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  or12 Unicode version

Theorem or12 509
Description: Swap two disjuncts. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 14-Nov-2012.)
Assertion
Ref Expression
or12  |-  ( (
ph  \/  ( ps  \/  ch ) )  <->  ( ps  \/  ( ph  \/  ch ) ) )

Proof of Theorem or12
StepHypRef Expression
1 pm1.5 508 . 2  |-  ( (
ph  \/  ( ps  \/  ch ) )  -> 
( ps  \/  ( ph  \/  ch ) ) )
2 pm1.5 508 . 2  |-  ( ( ps  \/  ( ph  \/  ch ) )  -> 
( ph  \/  ( ps  \/  ch ) ) )
31, 2impbii 180 1  |-  ( (
ph  \/  ( ps  \/  ch ) )  <->  ( ps  \/  ( ph  \/  ch ) ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    \/ wo 357
This theorem is referenced by:  orass  510  or32  513  or4  514  3orcoma  942  sotrieq  4357  ordzsl  4652  plydivex  19693
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-or 359
  Copyright terms: Public domain W3C validator