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Theorem or32 515
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 512 . 2  |-  ( ( ( ph  \/  ps )  \/  ch )  <->  (
ph  \/  ( ps  \/  ch ) ) )
2 or12 511 . 2  |-  ( (
ph  \/  ( ps  \/  ch ) )  <->  ( ps  \/  ( ph  \/  ch ) ) )
3 orcom 378 . 2  |-  ( ( ps  \/  ( ph  \/  ch ) )  <->  ( ( ph  \/  ch )  \/ 
ps ) )
41, 2, 33bitri 264 1  |-  ( ( ( ph  \/  ps )  \/  ch )  <->  ( ( ph  \/  ch )  \/  ps )
)
Colors of variables: wff set class
Syntax hints:    <-> wb 178    \/ wo 359
This theorem is referenced by:  sspsstri  3451  somo  4539  ordtri3  4619  psslinpr  8910  xrnepnf  10721  xrinfmss  10890  tosso  14467  lineunray  26083
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 179  df-or 361
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