Theorem cbvrexdva

Description: Rule used to change the bound variable in a restricted existential quantifier with implicit substitution. Deduction form. (Contributed by David Moews, 1-May-2017)

	Ref	Expression
Hypothesis	cbvraldva.1	|- ( ( ph /\ x = y ) -> ( ps <-> ch ) )
Assertion	cbvrexdva	|- ( ph -> ( E. x e. A ps <-> E. y e. A ch ) )

Proof

Step	Hyp	Ref	Expression
1		cbvraldva.1	|- ( ( ph /\ x = y ) -> ( ps <-> ch ) )
2		eqidd	|- ( ( ph /\ x = y ) -> A = A )
3	1 2	cbvrexdva2	|- ( ph -> ( E. x e. A ps <-> E. y e. A ch ) )