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Theorem 3an6 1262
Description: Analog of an4 797 for triple conjunction. (Contributed by Scott Fenton, 16-Mar-2011.) (Proof shortened by Andrew Salmon, 25-May-2011.)
Assertion
Ref Expression
3an6  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  th )  /\  ( ta 
/\  et ) )  <-> 
( ( ph  /\  ch  /\  ta )  /\  ( ps  /\  th  /\  et ) ) )

Proof of Theorem 3an6
StepHypRef Expression
1 an6 1261 . 2  |-  ( ( ( ph  /\  ch  /\ 
ta )  /\  ( ps  /\  th  /\  et ) )  <->  ( ( ph  /\  ps )  /\  ( ch  /\  th )  /\  ( ta  /\  et ) ) )
21bicomi 193 1  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  th )  /\  ( ta 
/\  et ) )  <-> 
( ( ph  /\  ch  /\  ta )  /\  ( ps  /\  th  /\  et ) ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ wa 358    /\ w3a 934
This theorem is referenced by:  poxp  6227  wfrlem4  24259  axcontlem8  24599  cgr3tr4  24675
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 177  df-an 360  df-3an 936
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