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Theorem or4 771
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 766 . . 3  |-  ( ( ps  \/  ( ch  \/  th ) )  <-> 
( ch  \/  ( ps  \/  th ) ) )
21orbi2i 762 . 2  |-  ( (
ph  \/  ( ps  \/  ( ch  \/  th ) ) )  <->  ( ph  \/  ( ch  \/  ( ps  \/  th ) ) ) )
3 orass 767 . 2  |-  ( ( ( ph  \/  ps )  \/  ( ch  \/  th ) )  <->  ( ph  \/  ( ps  \/  ( ch  \/  th ) ) ) )
4 orass 767 . 2  |-  ( ( ( ph  \/  ch )  \/  ( ps  \/  th ) )  <->  ( ph  \/  ( ch  \/  ( ps  \/  th ) ) ) )
52, 3, 43bitr4i 212 1  |-  ( ( ( ph  \/  ps )  \/  ( ch  \/  th ) )  <->  ( ( ph  \/  ch )  \/  ( ps  \/  th ) ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 105    \/ wo 708
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  or42  772  orordi  773  orordir  774  3or6  1323  swoer  6563  apcotr  8564
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