Theorem reubii

Description: Formula-building rule for restricted existential uniqueness quantifier (inference form). (Contributed by NM, 22-Oct-1999)

	Ref	Expression
Hypothesis	rmobii.1	$$⊢\phi \leftrightarrow \psi$$
Assertion	reubii	$$⊢\exists !x\in A\phi \leftrightarrow \exists !x\in A\psi$$

Proof

Step	Hyp	Ref	Expression
1		rmobii.1	$$⊢\phi \leftrightarrow \psi$$
2	1	a1i	$$⊢x\in A\to \left(\phi \leftrightarrow \psi \right)$$
3	2	reubiia	$$⊢\exists !x\in A\phi \leftrightarrow \exists !x\in A\psi$$