Theorem ralbid

Description: Formula-building rule for restricted universal quantifier (deduction form). (Contributed by NM, 27-Jun-1998)

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

Proof

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