Theorem rexbid

Description: Formula-building rule for restricted existential quantifier (deduction form). For a version based on fewer axioms see rexbidv . (Contributed by NM, 27-Jun-1998)

	Ref	Expression
Hypotheses	rexbid.1	|- F/ x ph
	rexbid.2	|- ( ph -> ( ps <-> ch ) )
Assertion	rexbid	|- ( ph -> ( E. x e. A ps <-> E. x e. A ch ) )

Proof

Step	Hyp	Ref	Expression
1		rexbid.1	|- F/ x ph
2		rexbid.2	|- ( ph -> ( ps <-> ch ) )
3	2	adantr	|- ( ( ph /\ x e. A ) -> ( ps <-> ch ) )
4	1 3	rexbida	|- ( ph -> ( E. x e. A ps <-> E. x e. A ch ) )