Theorem rmoeqdv

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

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

Proof

Step	Hyp	Ref	Expression
1		rmoeqdv.1	|- ( ph -> A = B )
2		rmoeq1	|- ( 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 ) )