Theorem 3anrot 924

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 262	. 2 |- ( ( ph /\ ( ps /\ ch ) ) <-> ( ( ps /\ ch ) /\ ph ) )
2		3anass 923	. 2 |- ( ( ph /\ ps /\ ch ) <-> ( ph /\ ( ps /\ ch ) ) )
3		df-3an 921	. 2 |- ( ( ps /\ ch /\ ph ) <-> ( ( ps /\ ch ) /\ ph ) )
4	1, 2, 3	3bitr4i 210	1 |- ( ( ph /\ ps /\ ch ) <-> ( ps /\ ch /\ ph ) )

Syntax hints:   /\ wa 102   <-> wb 103   /\ w3a 919

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115  df-3an 921

This theorem is referenced by:  3ancomb  927  3anrev  929  3simpc  937  caovlem2d  5713  nnmcan  6115  modmulconst  10227