Theorem 3an6 1409

Description: Analogue of an4 865 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

Step	Hyp	Ref	Expression
1		an6 1408	. 2 |- ( ( ( ph /\ ch /\ ta ) /\ ( ps /\ th /\ et ) ) <-> ( ( ph /\ ps ) /\ ( ch /\ th ) /\ ( ta /\ et ) ) )
2	1	bicomi 214	1 |- ( ( ( ph /\ ps ) /\ ( ch /\ th ) /\ ( ta /\ et ) ) <-> ( ( ph /\ ch /\ ta ) /\ ( ps /\ th /\ et ) ) )

Syntax hints:   <-> wb 196   /\ wa 384   /\ w3a 1037

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 197  df-an 386  df-3an 1039

This theorem is referenced by:  an33rean  1446  f13dfv  6530  poxp  7289  wfrlem4  7418  cotr2g  13715  axcontlem8  25851  cplgr3v  26331  cgr3tr4  32159