Theorem rexeqi

Description: Equality inference for restricted existential quantifier. (Contributed by Mario Carneiro, 23-Apr-2015)

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

Proof

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