Theorem 3anrot 973

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 972	. 2 |- ( ( ph /\ ps /\ ch ) <-> ( ph /\ ( ps /\ ch ) ) )
3		df-3an 970	. 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 968

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

This theorem depends on definitions:  df-bi 116  df-3an 970

This theorem is referenced by:  3ancomb  976  3anrev  978  3simpc  986  caovlem2d  6034  nnmcan  6487  modmulconst  11763  xmetpsmet  13009  comet  13139  lgsdi  13578