Theorem 3ancomb 781

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 780	. 2 |- ((ph /\ ps /\ ch) <-> (ps /\ ph /\ ch))
2		3anrot 778	. 2 |- ((ps /\ ph /\ ch) <-> (ph /\ ch /\ ps))
3	1, 2	bitr 173	1 |- ((ph /\ ps /\ ch) <-> (ph /\ ch /\ ps))

Syntax hints:   <-> wb 146   /\ w3a 773

This theorem is referenced by:  3simpb 784  abl23 8040  abldivdiv 8045  abldiv23 8047  nvsubsub23 8222  efifolem2 8638  cnvhmph 10414  hmphsyma 10415

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 775

Copyright terms: Public domain