Theorem bnj887

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

	Ref	Expression
Hypotheses	bnj887.1	|- ( ph <-> ph' )
	bnj887.2	|- ( ps <-> ps' )
	bnj887.3	|- ( ch <-> ch' )
	bnj887.4	|- ( th <-> th' )
Assertion	bnj887	|- ( ( ph /\ ps /\ ch /\ th ) <-> ( ph' /\ ps' /\ ch' /\ th' ) )

Proof

Step	Hyp	Ref	Expression
1		bnj887.1	|- ( ph <-> ph' )
2		bnj887.2	|- ( ps <-> ps' )
3		bnj887.3	|- ( ch <-> ch' )
4		bnj887.4	|- ( th <-> th' )
5	1 2 3	3anbi123i	|- ( ( ph /\ ps /\ ch ) <-> ( ph' /\ ps' /\ ch' ) )
6	5 4	anbi12i	|- ( ( ( ph /\ ps /\ ch ) /\ th ) <-> ( ( ph' /\ ps' /\ ch' ) /\ th' ) )
7		df-bnj17	|- ( ( ph /\ ps /\ ch /\ th ) <-> ( ( ph /\ ps /\ ch ) /\ th ) )
8		df-bnj17	|- ( ( ph' /\ ps' /\ ch' /\ th' ) <-> ( ( ph' /\ ps' /\ ch' ) /\ th' ) )
9	6 7 8	3bitr4i	|- ( ( ph /\ ps /\ ch /\ th ) <-> ( ph' /\ ps' /\ ch' /\ th' ) )