Theorem bnj312

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

	Ref	Expression
Assertion	bnj312	|- ( ( ph /\ ps /\ ch /\ th ) <-> ( ps /\ ph /\ ch /\ th ) )

Proof

Step	Hyp	Ref	Expression
1		3ancoma	|- ( ( ph /\ ps /\ ch ) <-> ( ps /\ ph /\ ch ) )
2	1	anbi1i	|- ( ( ( ph /\ ps /\ ch ) /\ th ) <-> ( ( ps /\ ph /\ ch ) /\ th ) )
3		df-bnj17	|- ( ( ph /\ ps /\ ch /\ th ) <-> ( ( ph /\ ps /\ ch ) /\ th ) )
4		df-bnj17	|- ( ( ps /\ ph /\ ch /\ th ) <-> ( ( ps /\ ph /\ ch ) /\ th ) )
5	2 3 4	3bitr4i	|- ( ( ph /\ ps /\ ch /\ th ) <-> ( ps /\ ph /\ ch /\ th ) )