Theorem an42

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

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

Proof

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