Theorem 3ancomb 783

Description: Commutation law for triple conjunction.

Assertion

Ref	Expression
3ancomb	|- ((ph /\ ps /\ ch) <-> (ph /\ ch /\ ps))

Proof of Theorem 3ancomb

Step	Hyp	Ref	Expression
1		3ancoma 782	. 2 |- ((ph /\ ps /\ ch) <-> (ps /\ ph /\ ch))
2		3anrot 780	. 2 |- ((ps /\ ph /\ ch) <-> (ph /\ ch /\ ps))
3	1, 2	bitr 173	1 |- ((ph /\ ps /\ ch) <-> (ph /\ ch /\ ps))

Syntax hints:   <-> wb 146   /\ w3a 775

This theorem is referenced by:  3simpb 786  abl23 8104  abldivdiv 8108  abldiv23 8110  nvsubsub23 8282  efifolem2 8723  cnvhmph 10527  hmphsyma 10528

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225  df-3an 777

Copyright terms: Public domain