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 ∈ 𝑉 → ∃ 𝑥 𝑥 = 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		elissetv	⊢ ( 𝐴 ∈ 𝑉 → ∃ 𝑧 𝑧 = 𝐴 )
2		iseqsetv-clel	⊢ ( ∃ 𝑧 𝑧 = 𝐴 ↔ ∃ 𝑥 𝑥 = 𝐴 )
3	1 2	sylib	⊢ ( 𝐴 ∈ 𝑉 → ∃ 𝑥 𝑥 = 𝐴 )