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Theorem 3or6 1265
Description: Analog of or4 515 for triple conjunction. (Contributed by Scott Fenton, 16-Mar-2011.)
Assertion
Ref Expression
3or6  |-  ( ( ( ph  \/  ps )  \/  ( ch  \/  th )  \/  ( ta  \/  et ) )  <-> 
( ( ph  \/  ch  \/  ta )  \/  ( ps  \/  th  \/  et ) ) )

Proof of Theorem 3or6
StepHypRef Expression
1 or4 515 . . 3  |-  ( ( ( ( ph  \/  ch )  \/  ta )  \/  ( ( ps  \/  th )  \/  et ) )  <->  ( (
( ph  \/  ch )  \/  ( ps  \/  th ) )  \/  ( ta  \/  et ) ) )
2 or4 515 . . . 4  |-  ( ( ( ph  \/  ch )  \/  ( ps  \/  th ) )  <->  ( ( ph  \/  ps )  \/  ( ch  \/  th ) ) )
32orbi1i 507 . . 3  |-  ( ( ( ( ph  \/  ch )  \/  ( ps  \/  th ) )  \/  ( ta  \/  et ) )  <->  ( (
( ph  \/  ps )  \/  ( ch  \/  th ) )  \/  ( ta  \/  et ) ) )
41, 3bitr2i 242 . 2  |-  ( ( ( ( ph  \/  ps )  \/  ( ch  \/  th ) )  \/  ( ta  \/  et ) )  <->  ( (
( ph  \/  ch )  \/  ta )  \/  ( ( ps  \/  th )  \/  et ) ) )
5 df-3or 937 . 2  |-  ( ( ( ph  \/  ps )  \/  ( ch  \/  th )  \/  ( ta  \/  et ) )  <-> 
( ( ( ph  \/  ps )  \/  ( ch  \/  th ) )  \/  ( ta  \/  et ) ) )
6 df-3or 937 . . 3  |-  ( (
ph  \/  ch  \/  ta )  <->  ( ( ph  \/  ch )  \/  ta ) )
7 df-3or 937 . . 3  |-  ( ( ps  \/  th  \/  et )  <->  ( ( ps  \/  th )  \/  et ) )
86, 7orbi12i 508 . 2  |-  ( ( ( ph  \/  ch  \/  ta )  \/  ( ps  \/  th  \/  et ) )  <->  ( (
( ph  \/  ch )  \/  ta )  \/  ( ( ps  \/  th )  \/  et ) ) )
94, 5, 83bitr4i 269 1  |-  ( ( ( ph  \/  ps )  \/  ( ch  \/  th )  \/  ( ta  \/  et ) )  <-> 
( ( ph  \/  ch  \/  ta )  \/  ( ps  \/  th  \/  et ) ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    \/ wo 358    \/ w3o 935
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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