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Theorem or42 515
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 514 . 2  |-  ( ( ( ph  \/  ps )  \/  ( ch  \/  th ) )  <->  ( ( ph  \/  ch )  \/  ( ps  \/  th ) ) )
2 orcom 376 . . 3  |-  ( ( ps  \/  th )  <->  ( th  \/  ps )
)
32orbi2i 505 . 2  |-  ( ( ( ph  \/  ch )  \/  ( ps  \/  th ) )  <->  ( ( ph  \/  ch )  \/  ( th  \/  ps ) ) )
41, 3bitri 240 1  |-  ( ( ( ph  \/  ps )  \/  ( ch  \/  th ) )  <->  ( ( ph  \/  ch )  \/  ( th  \/  ps ) ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    \/ wo 357
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
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