Theorem 3anrot 985

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 266	. 2 |- ( ( ph /\ ( ps /\ ch ) ) <-> ( ( ps /\ ch ) /\ ph ) )
2		3anass 984	. 2 |- ( ( ph /\ ps /\ ch ) <-> ( ph /\ ( ps /\ ch ) ) )
3		df-3an 982	. 2 |- ( ( ps /\ ch /\ ph ) <-> ( ( ps /\ ch ) /\ ph ) )
4	1, 2, 3	3bitr4i 212	1 |- ( ( ph /\ ps /\ ch ) <-> ( ps /\ ch /\ ph ) )

Syntax hints:   /\ wa 104   <-> wb 105   /\ w3a 980

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 982

This theorem is referenced by:  3ancomb  988  3anrev  990  3simpc  998  caovlem2d  6120  nnmcan  6586  modmulconst  12005  srgrmhm  13626  xmetpsmet  14689  comet  14819  lgsdi  15362