Theorem rexeqdv

Description: Equality deduction for restricted existential quantifier. (Contributed by NM, 14-Jan-2007)

	Ref	Expression
Hypothesis	raleq1d.1	|- ( ph -> A = B )
Assertion	rexeqdv	|- ( ph -> ( E. x e. A ps <-> E. x e. B ps ) )

Proof

Step	Hyp	Ref	Expression
1		raleq1d.1	|- ( ph -> A = B )
2		rexeq	|- ( A = B -> ( E. x e. A ps <-> E. x e. B ps ) )
3	1 2	syl	|- ( ph -> ( E. x e. A ps <-> E. x e. B ps ) )