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 e. V -> E. x x = A )

Proof

Step	Hyp	Ref	Expression
1		elissetv	|- ( A e. V -> E. y y = A )
2		vextru	|- y e. { z | T. }
3	2	issetlem	|- ( A e. { z | T. } <-> E. y y = A )
4		vextru	|- x e. { z | T. }
5	4	issetlem	|- ( A e. { z | T. } <-> E. x x = A )
6	3 5	bitr3i	|- ( E. y y = A <-> E. x x = A )
7	1 6	sylib	|- ( A e. V -> E. x x = A )