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Theorem 3orcomb 975
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 387 . . 3  |-  ( ( ps  \/  ch )  <->  ( ch  \/  ps )
)
21orbi2i 519 . 2  |-  ( (
ph  \/  ( ps  \/  ch ) )  <->  ( ph  \/  ( ch  \/  ps ) ) )
3 3orass 968 . 2  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ph  \/  ( ps  \/  ch ) ) )
4 3orass 968 . 2  |-  ( (
ph  \/  ch  \/  ps )  <->  ( ph  \/  ( ch  \/  ps ) ) )
52, 3, 43bitr4i 277 1  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ph  \/  ch  \/  ps ) )
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:  eueq3  3133  swoso  7131  swrdnd  12325  colcom  22991  lncom  23028  soseq  27714  colinearperm1  28092  ordelordALT  31242  ordelordALTVD  31601
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