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Metamath Proof Explorer

Theorem elissetv

Description: An element of a class exists. Version of elisset with a disjoint variable condition on V , x , avoiding df-clab . Prefer its use over elisset when sufficient (for instance in usages where x is a dummy variable). (Contributed by BJ, 14-Sep-2019)

		Ref	Expression
	Assertion	elissetv	$⊢ A \in V \to \exists x x = A$

Proof

Step	Hyp	Ref	Expression
1		dfclel	$⊢ A \in V \leftrightarrow \exists x (x = A \land x \in V)$
2		exsimpl	$⊢ \exists x (x = A \land x \in V) \to \exists x x = A$
3	1 2	sylbi	$⊢ A \in V \to \exists x x = A$