MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  or32 Unicode version

Theorem or32 513
Description: A rearrangement of disjuncts. (Contributed by NM, 18-Oct-1995.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
or32  |-  ( ( ( ph  \/  ps )  \/  ch )  <->  ( ( ph  \/  ch )  \/  ps )
)

Proof of Theorem or32
StepHypRef Expression
1 orass 510 . 2  |-  ( ( ( ph  \/  ps )  \/  ch )  <->  (
ph  \/  ( ps  \/  ch ) ) )
2 or12 509 . 2  |-  ( (
ph  \/  ( ps  \/  ch ) )  <->  ( ps  \/  ( ph  \/  ch ) ) )
3 orcom 376 . 2  |-  ( ( ps  \/  ( ph  \/  ch ) )  <->  ( ( ph  \/  ch )  \/ 
ps ) )
41, 2, 33bitri 262 1  |-  ( ( ( ph  \/  ps )  \/  ch )  <->  ( ( ph  \/  ch )  \/  ps )
)
Colors of variables: wff set class
Syntax hints:    <-> wb 176    \/ wo 357
This theorem is referenced by:  sspsstri  3278  somo  4348  ordtri3  4428  psslinpr  8655  xrnepnf  10461  xrinfmss  10628  tosso  14142  lineunray  24770
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