Theorem reueqi

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

	Ref	Expression
Hypothesis	reueqi.1	|- A = B
Assertion	reueqi	|- ( E! x e. A ps <-> E! x e. B ps )

Proof

Step	Hyp	Ref	Expression
1		reueqi.1	|- A = B
2	1	eleq2i	|- ( x e. A <-> x e. B )
3	2	anbi1i	|- ( ( x e. A /\ ps ) <-> ( x e. B /\ ps ) )
4	3	eubii	|- ( E! x ( x e. A /\ ps ) <-> E! x ( x e. B /\ ps ) )
5		df-reu	|- ( E! x e. A ps <-> E! x ( x e. A /\ ps ) )
6		df-reu	|- ( E! x e. B ps <-> E! x ( x e. B /\ ps ) )
7	4 5 6	3bitr4i	|- ( E! x e. A ps <-> E! x e. B ps )