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Metamath Proof Explorer

Theorem euabex

Description: The abstraction of a wff with existential uniqueness exists. (Contributed by NM, 25-Nov-1994)

		Ref	Expression
	Assertion	euabex	$⊢ \exists! x φ \to \{x \| φ\} \in V$

Step	Hyp	Ref	Expression
1		eumo	$⊢ \exists! x φ \to \exists^{*} x φ$
2		moabex	$⊢ \exists^{*} x φ \to \{x \| φ\} \in V$
3	1 2	syl	$⊢ \exists! x φ \to \{x \| φ\} \in V$