Theorem 3anrot 890

Description: Rotation law for triple conjunction. (Contributed by NM, 8-Apr-1994.)

Assertion

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

Proof of Theorem 3anrot

Step	Hyp	Ref	Expression
1		ancom 253	. 2 |- ( ( ph /\ ( ps /\ ch ) ) <-> ( ( ps /\ ch ) /\ ph ) )
2		3anass 889	. 2 |- ( ( ph /\ ps /\ ch ) <-> ( ph /\ ( ps /\ ch ) ) )
3		df-3an 887	. 2 |- ( ( ps /\ ch /\ ph ) <-> ( ( ps /\ ch ) /\ ph ) )
4	1, 2, 3	3bitr4i 201	1 |- ( ( ph /\ ps /\ ch ) <-> ( ps /\ ch /\ ph ) )

Syntax hints:   /\ wa 97   <-> wb 98   /\ w3a 885

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110  df-3an 887

This theorem is referenced by:  3ancomb  893  3anrev  895  3simpc  903  caovlem2d  5693  nnmcan  6092