Theorem reueqdv

Description: Formula-building rule for restricted existential uniqueness quantifier. Deduction form. (Contributed by GG, 1-Sep-2025)

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

Proof

Step	Hyp	Ref	Expression
1		reueqdv.1	|- ( ph -> A = B )
2		reueq1	|- ( 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 ) )