Theorem reueqbii

Description: Equality inference for restricted existential uniqueness quantifier. (Contributed by GG, 1-Sep-2025)

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

Proof

Step	Hyp	Ref	Expression
1		reueqbii.1	|- A = B
2		reueqbii.2	|- ( ps <-> ch )
3	1	eleq2i	|- ( x e. A <-> x e. B )
4	3 2	anbi12i	|- ( ( x e. A /\ ps ) <-> ( x e. B /\ ch ) )
5	4	eubii	|- ( E! x ( x e. A /\ ps ) <-> E! x ( x e. B /\ ch ) )
6		df-reu	|- ( E! x e. A ps <-> E! x ( x e. A /\ ps ) )
7		df-reu	|- ( E! x e. B ch <-> E! x ( x e. B /\ ch ) )
8	5 6 7	3bitr4i	|- ( E! x e. A ps <-> E! x e. B ch )