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Theorem or4 516
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 511 . . 3  |-  ( ( ps  \/  ( ch  \/  th ) )  <-> 
( ch  \/  ( ps  \/  th ) ) )
21orbi2i 507 . 2  |-  ( (
ph  \/  ( ps  \/  ( ch  \/  th ) ) )  <->  ( ph  \/  ( ch  \/  ( ps  \/  th ) ) ) )
3 orass 512 . 2  |-  ( ( ( ph  \/  ps )  \/  ( ch  \/  th ) )  <->  ( ph  \/  ( ps  \/  ( ch  \/  th ) ) ) )
4 orass 512 . 2  |-  ( ( ( ph  \/  ch )  \/  ( ps  \/  th ) )  <->  ( ph  \/  ( ch  \/  ( ps  \/  th ) ) ) )
52, 3, 43bitr4i 270 1  |-  ( ( ( ph  \/  ps )  \/  ( ch  \/  th ) )  <->  ( ( ph  \/  ch )  \/  ( ps  \/  th ) ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 178    \/ wo 359
This theorem is referenced by:  or42  517  orordi  518  orordir  519  3or6  1266  swoer  6936  xmullem2  10849
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 179  df-or 361
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