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Theorem 3an6 1228
Description: Analog of an4 528 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 1227 . 2  |-  ( ( ( ph  /\  ch  /\ 
ta )  /\  ( ps  /\  th  /\  et ) )  <->  ( ( ph  /\  ps )  /\  ( ch  /\  th )  /\  ( ta  /\  et ) ) )
21bicomi 127 1  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  th )  /\  ( ta 
/\  et ) )  <-> 
( ( ph  /\  ch  /\  ta )  /\  ( ps  /\  th  /\  et ) ) )
Colors of variables: wff set class
Syntax hints:    /\ wa 101    <-> wb 102    /\ w3a 896
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by:  poxp  5881
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