Theorem an42 866

Description: Rearrangement of 4 conjuncts. (Contributed by NM, 7-Feb-1996.)

Assertion

Ref	Expression
an42	|- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) <-> ( ( ph /\ ch ) /\ ( th /\ ps ) ) )

Proof of Theorem an42

Step	Hyp	Ref	Expression
1		an4 865	. 2 |- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) <-> ( ( ph /\ ch ) /\ ( ps /\ th ) ) )
2		ancom 466	. . 3 |- ( ( ps /\ th ) <-> ( th /\ ps ) )
3	2	anbi2i 730	. 2 |- ( ( ( ph /\ ch ) /\ ( ps /\ th ) ) <-> ( ( ph /\ ch ) /\ ( th /\ ps ) ) )
4	1, 3	bitri 264	1 |- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) <-> ( ( ph /\ ch ) /\ ( th /\ ps ) ) )

Syntax hints:   <-> wb 196   /\ wa 384

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386

This theorem is referenced by:  an43  867  brecop2  7841  supmo  8358  infmo  8401  aceq1  8940  dfiso2  16432  eulerpartlemt0  30431  isbasisrelowllem1  33203  isbasisrelowllem2  33204  ifp1bi  37847