Theorem bnj257

Description: /\ -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Assertion	bnj257	|- ( ( ph /\ ps /\ ch /\ th ) <-> ( ph /\ ps /\ th /\ ch ) )

Proof

Step	Hyp	Ref	Expression
1		ancom	|- ( ( ch /\ th ) <-> ( th /\ ch ) )
2	1	anbi2i	|- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) <-> ( ( ph /\ ps ) /\ ( th /\ ch ) ) )
3		bnj256	|- ( ( ph /\ ps /\ ch /\ th ) <-> ( ( ph /\ ps ) /\ ( ch /\ th ) ) )
4		bnj256	|- ( ( ph /\ ps /\ th /\ ch ) <-> ( ( ph /\ ps ) /\ ( th /\ ch ) ) )
5	2 3 4	3bitr4i	|- ( ( ph /\ ps /\ ch /\ th ) <-> ( ph /\ ps /\ th /\ ch ) )