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

Step	Hyp	Ref	Expression
1		an6 1261	. 2 |- (((ph /\ ch /\ ta) /\ (ps /\ th /\ et)) <-> ((ph /\ ps) /\ (ch /\ th) /\ (ta /\ et)))
2	1	bicomi 193	1 |- (((ph /\ ps) /\ (ch /\ th) /\ (ta /\ et)) <-> ((ph /\ ch /\ ta) /\ (ps /\ th /\ et)))

Syntax hints:   <-> wb 176   /\ wa 358   /\ w3a 934

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 177  df-an 360  df-3an 936

This theorem is referenced by:  sfin112  4530  sfinltfin  4536