Theorem reueqbidva

Description: Formula-building rule for restricted existential uniqueness quantifier. Deduction form. General version of reueqbidv . (Contributed by Zhi Wang, 20-Nov-2025)

	Ref	Expression
Hypotheses	reueqbidva.1	|- ( ph -> A = B )
	reueqbidva.2	|- ( ( ph /\ x e. A ) -> ( ps <-> ch ) )
Assertion	reueqbidva	|- ( ph -> ( E! x e. A ps <-> E! x e. B ch ) )

Proof

Step	Hyp	Ref	Expression
1		reueqbidva.1	|- ( ph -> A = B )
2		reueqbidva.2	|- ( ( ph /\ x e. A ) -> ( ps <-> ch ) )
3	2	reubidva	|- ( ph -> ( E! x e. A ps <-> E! x e. A ch ) )
4	1	reueqdv	|- ( ph -> ( E! x e. A ch <-> E! x e. B ch ) )
5	3 4	bitrd	|- ( ph -> ( E! x e. A ps <-> E! x e. B ch ) )