Theorem reubidv

Description: Formula-building rule for restricted existential quantifier (deduction form). (Contributed by NM, 17-Oct-1996)

	Ref	Expression
Hypothesis	reubidv.1	|- ( ph -> ( ps <-> ch ) )
Assertion	reubidv	|- ( ph -> ( E! x e. A ps <-> E! x e. A ch ) )

Proof

Step	Hyp	Ref	Expression
1		reubidv.1	|- ( ph -> ( ps <-> ch ) )
2	1	adantr	|- ( ( ph /\ x e. A ) -> ( ps <-> ch ) )
3	2	reubidva	|- ( ph -> ( E! x e. A ps <-> E! x e. A ch ) )