Theorem ralbiia

Description: Inference adding restricted universal quantifier to both sides of an equivalence. (Contributed by NM, 26-Nov-2000)

	Ref	Expression
Hypothesis	ralbiia.1	|- ( x e. A -> ( ph <-> ps ) )
Assertion	ralbiia	|- ( A. x e. A ph <-> A. x e. A ps )

Proof

Step	Hyp	Ref	Expression
1		ralbiia.1	|- ( x e. A -> ( ph <-> ps ) )
2	1	pm5.74i	|- ( ( x e. A -> ph ) <-> ( x e. A -> ps ) )
3	2	ralbii2	|- ( A. x e. A ph <-> A. x e. A ps )