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Theorem or4 721
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 716 . . 3  |-  ( ( ps  \/  ( ch  \/  th ) )  <-> 
( ch  \/  ( ps  \/  th ) ) )
21orbi2i 712 . 2  |-  ( (
ph  \/  ( ps  \/  ( ch  \/  th ) ) )  <->  ( ph  \/  ( ch  \/  ( ps  \/  th ) ) ) )
3 orass 717 . 2  |-  ( ( ( ph  \/  ps )  \/  ( ch  \/  th ) )  <->  ( ph  \/  ( ps  \/  ( ch  \/  th ) ) ) )
4 orass 717 . 2  |-  ( ( ( ph  \/  ch )  \/  ( ps  \/  th ) )  <->  ( ph  \/  ( ch  \/  ( ps  \/  th ) ) ) )
52, 3, 43bitr4i 210 1  |-  ( ( ( ph  \/  ps )  \/  ( ch  \/  th ) )  <->  ( ( ph  \/  ch )  \/  ( ps  \/  th ) ) )
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:  or42  722  orordi  723  orordir  724  3or6  1255  swoer  6200  apcotr  7774
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