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	$$⊢\phi \to A=B$$
Assertion	rmoeqdv	$$⊢\phi \to \left({\exists }^{*}x\in A\psi \leftrightarrow {\exists }^{*}x\in B\psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		rmoeqdv.1	$$⊢\phi \to A=B$$
2		rmoeq1	$$⊢A=B\to \left({\exists }^{*}x\in A\psi \leftrightarrow {\exists }^{*}x\in B\psi \right)$$
3	1 2	syl	$$⊢\phi \to \left({\exists }^{*}x\in A\psi \leftrightarrow {\exists }^{*}x\in B\psi \right)$$