Theorem 3anrot 948

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 264	. 2 |- ( ( ph /\ ( ps /\ ch ) ) <-> ( ( ps /\ ch ) /\ ph ) )
2		3anass 947	. 2 |- ( ( ph /\ ps /\ ch ) <-> ( ph /\ ( ps /\ ch ) ) )
3		df-3an 945	. 2 |- ( ( ps /\ ch /\ ph ) <-> ( ( ps /\ ch ) /\ ph ) )
4	1, 2, 3	3bitr4i 211	1 |- ( ( ph /\ ps /\ ch ) <-> ( ps /\ ch /\ ph ) )

Syntax hints:   /\ wa 103   <-> wb 104   /\ w3a 943

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-3an 945

This theorem is referenced by:  3ancomb  951  3anrev  953  3simpc  961  caovlem2d  5915  nnmcan  6366  modmulconst  11366  xmetpsmet  12351  comet  12481