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Metamath Proof Explorer

Theorem reubii

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

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

Step	Hyp	Ref	Expression
1		rmobii.1	$⊢ φ \leftrightarrow ψ$
2	1	a1i	$⊢ x \in A \to (φ \leftrightarrow ψ)$
3	2	reubiia	$⊢ \exists! x \in A φ \leftrightarrow \exists! x \in A ψ$