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Theorem or42 761
Description: Rearrangement of 4 disjuncts. (Contributed by NM, 10-Jan-2005.)
Assertion
Ref Expression
or42  |-  ( ( ( ph  \/  ps )  \/  ( ch  \/  th ) )  <->  ( ( ph  \/  ch )  \/  ( th  \/  ps ) ) )

Proof of Theorem or42
StepHypRef Expression
1 or4 760 . 2  |-  ( ( ( ph  \/  ps )  \/  ( ch  \/  th ) )  <->  ( ( ph  \/  ch )  \/  ( ps  \/  th ) ) )
2 orcom 717 . . 3  |-  ( ( ps  \/  th )  <->  ( th  \/  ps )
)
32orbi2i 751 . 2  |-  ( ( ( ph  \/  ch )  \/  ( ps  \/  th ) )  <->  ( ( ph  \/  ch )  \/  ( th  \/  ps ) ) )
41, 3bitri 183 1  |-  ( ( ( ph  \/  ps )  \/  ( ch  \/  th ) )  <->  ( ( ph  \/  ch )  \/  ( th  \/  ps ) ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 104    \/ wo 697
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  reapcotr  8367
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