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Theorem 3an6 1300
Description: Analog of an4 820 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 1299 . 2  |-  ( ( ( ph  /\  ch  /\ 
ta )  /\  ( ps  /\  th  /\  et ) )  <->  ( ( ph  /\  ps )  /\  ( ch  /\  th )  /\  ( ta  /\  et ) ) )
21bicomi 202 1  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  th )  /\  ( ta 
/\  et ) )  <-> 
( ( ph  /\  ch  /\  ta )  /\  ( ps  /\  th  /\  et ) ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    /\ wa 369    /\ w3a 965
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-an 371  df-3an 967
This theorem is referenced by:  an33rean  1333  poxp  6787  axcontlem8  23362  cusgra3v  23517  wfrlem4  27864  cgr3tr4  28220  f13dfv  30288
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