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Metamath Proof Explorer

Theorem elisset

Description: An element of a class exists. Use elissetv instead when sufficient (for instance in usages where x is a dummy variable). (Contributed by NM, 1-May-1995) Reduce dependencies on axioms. (Revised by BJ, 29-Apr-2019)

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

Proof

Step	Hyp	Ref	Expression
1		elissetv	$⊢ A \in V \to \exists z z = A$
2		iseqsetv-clel	$⊢ \exists z z = A \leftrightarrow \exists x x = A$
3	1 2	sylib	$⊢ A \in V \to \exists x x = A$