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Theorem 3orcomb 946
Description: Commutation law for triple disjunction. (Contributed by Scott Fenton, 20-Apr-2011.)
Assertion
Ref Expression
3orcomb  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ph  \/  ch  \/  ps ) )

Proof of Theorem 3orcomb
StepHypRef Expression
1 orcom 377 . . 3  |-  ( ( ps  \/  ch )  <->  ( ch  \/  ps )
)
21orbi2i 506 . 2  |-  ( (
ph  \/  ( ps  \/  ch ) )  <->  ( ph  \/  ( ch  \/  ps ) ) )
3 3orass 939 . 2  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ph  \/  ( ps  \/  ch ) ) )
4 3orass 939 . 2  |-  ( (
ph  \/  ch  \/  ps )  <->  ( ph  \/  ( ch  \/  ps ) ) )
52, 3, 43bitr4i 269 1  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ph  \/  ch  \/  ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    \/ wo 358    \/ w3o 935
This theorem is referenced by:  eueq3  3109  swoso  6936  soseq  25529  colinearperm1  25996  swrdnd  28182  ordelordALT  28622  ordelordALTVD  28979
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 178  df-or 360  df-3or 937
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