MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  3orcoma Structured version   Unicode version

Theorem 3orcoma 973
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 523 . 2  |-  ( (
ph  \/  ( ps  \/  ch ) )  <->  ( ps  \/  ( ph  \/  ch ) ) )
2 3orass 968 . 2  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ph  \/  ( ps  \/  ch ) ) )
3 3orass 968 . 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 368    \/ w3o 964
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 370  df-3or 966
This theorem is referenced by:  cadcomb  1439  eliccioo  26278
  Copyright terms: Public domain W3C validator