Theorem 3ancomb 943

Description: Commutation law for triple conjunction. (Contributed by NM, 21-Apr-1994.)

Assertion

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

Proof of Theorem 3ancomb

Step	Hyp	Ref	Expression
1		3ancoma 941	. 2 |- ((ph /\ ps /\ ch) <-> (ps /\ ph /\ ch))
2		3anrot 939	. 2 |- ((ps /\ ph /\ ch) <-> (ph /\ ch /\ ps))
3	1, 2	bitri 240	1 |- ((ph /\ ps /\ ch) <-> (ph /\ ch /\ ps))

Syntax hints:   <-> wb 176   /\ 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:  3simpb  953