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Theorem 3orcoma 980
Description: Commutation law for triple disjunction. (Contributed by Mario Carneiro, 4-Sep-2016.)
Assertion
Ref Expression
3orcoma  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ps  \/  ph  \/  ch ) )

Proof of Theorem 3orcoma
StepHypRef Expression
1 or12 521 . 2  |-  ( (
ph  \/  ( ps  \/  ch ) )  <->  ( ps  \/  ( ph  \/  ch ) ) )
2 3orass 975 . 2  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ph  \/  ( ps  \/  ch ) ) )
3 3orass 975 . 2  |-  ( ( ps  \/  ph  \/  ch )  <->  ( ps  \/  ( ph  \/  ch )
) )
41, 2, 33bitr4i 277 1  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ps  \/  ph  \/  ch ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    \/ wo 366    \/ w3o 971
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 185  df-or 368  df-3or 973
This theorem is referenced by:  cadcombOLD  1479  eliccioo  27960
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