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Theorem 3an6 1309
Description: Analog of an4 822 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 1308 . 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 973
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 975
This theorem is referenced by:  an33rean  1342  f13dfv  6166  poxp  6892  axcontlem8  23950  cusgra3v  24140  wfrlem4  28923  cgr3tr4  29279
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