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Theorem or4 514
Description: Rearrangement of 4 disjuncts. (Contributed by NM, 12-Aug-1994.)
Assertion
Ref Expression
or4  |-  ( ( ( ph  \/  ps )  \/  ( ch  \/  th ) )  <->  ( ( ph  \/  ch )  \/  ( ps  \/  th ) ) )

Proof of Theorem or4
StepHypRef Expression
1 or12 509 . . 3  |-  ( ( ps  \/  ( ch  \/  th ) )  <-> 
( ch  \/  ( ps  \/  th ) ) )
21orbi2i 505 . 2  |-  ( (
ph  \/  ( ps  \/  ( ch  \/  th ) ) )  <->  ( ph  \/  ( ch  \/  ( ps  \/  th ) ) ) )
3 orass 510 . 2  |-  ( ( ( ph  \/  ps )  \/  ( ch  \/  th ) )  <->  ( ph  \/  ( ps  \/  ( ch  \/  th ) ) ) )
4 orass 510 . 2  |-  ( ( ( ph  \/  ch )  \/  ( ps  \/  th ) )  <->  ( ph  \/  ( ch  \/  ( ps  \/  th ) ) ) )
52, 3, 43bitr4i 268 1  |-  ( ( ( ph  \/  ps )  \/  ( ch  \/  th ) )  <->  ( ( ph  \/  ch )  \/  ( ps  \/  th ) ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    \/ wo 357
This theorem is referenced by:  or42  515  orordi  516  orordir  517  3or6  1263  swoer  6688  xmullem2  10585
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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