Theorem raleqi

Description: Equality inference for restricted universal quantifier. (Contributed by Paul Chapman, 22-Jun-2011)

	Ref	Expression
Hypothesis	raleq1i.1	|- A = B
Assertion	raleqi	|- ( A. x e. A ph <-> A. x e. B ph )

Proof

Step	Hyp	Ref	Expression
1		raleq1i.1	|- A = B
2		raleq	|- ( A = B -> ( A. x e. A ph <-> A. x e. B ph ) )
3	1 2	ax-mp	|- ( A. x e. A ph <-> A. x e. B ph )