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Theorem 3orcoma 944
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 510 . 2  |-  ( (
ph  \/  ( ps  \/  ch ) )  <->  ( ps  \/  ( ph  \/  ch ) ) )
2 3orass 939 . 2  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ph  \/  ( ps  \/  ch ) ) )
3 3orass 939 . 2  |-  ( ( ps  \/  ph  \/  ch )  <->  ( ps  \/  ( ph  \/  ch )
) )
41, 2, 33bitr4i 269 1  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ps  \/  ph  \/  ch ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    \/ wo 358    \/ w3o 935
This theorem is referenced by:  cadcomb  1405  eliccioo  24177
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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