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Theorem or32 720
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 717 . 2  |-  ( ( ( ph  \/  ps )  \/  ch )  <->  (
ph  \/  ( ps  \/  ch ) ) )
2 or12 716 . 2  |-  ( (
ph  \/  ( ps  \/  ch ) )  <->  ( ps  \/  ( ph  \/  ch ) ) )
3 orcom 680 . 2  |-  ( ( ps  \/  ( ph  \/  ch ) )  <->  ( ( ph  \/  ch )  \/ 
ps ) )
41, 2, 33bitri 204 1  |-  ( ( ( ph  \/  ps )  \/  ch )  <->  ( ( ph  \/  ch )  \/  ps )
)
Colors of variables: wff set class
Syntax hints:    <-> wb 103    \/ wo 662
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  xrnepnf  8930
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