Theorem bj-isseti

Description: Version of isseti with a class variable V in the hypothesis instead of _V for extra generality. This is indeed more general than isseti as long as elex is not available (and the non-dependence of bj-isseti on special properties of the universal class _V is obvious). Use bj-issetiv instead when sufficient (in particular when V is substituted for _V ). (Contributed by BJ, 13-Jun-2019) (Proof modification is discouraged.)

	Ref	Expression
Hypothesis	bj-isseti.1	⊢ 𝐴 ∈ 𝑉
Assertion	bj-isseti	⊢ ∃ 𝑥 𝑥 = 𝐴

Proof

Step	Hyp	Ref	Expression
1		bj-isseti.1	⊢ 𝐴 ∈ 𝑉
2		elisset	⊢ ( 𝐴 ∈ 𝑉 → ∃ 𝑥 𝑥 = 𝐴 )
3	1 2	ax-mp	⊢ ∃ 𝑥 𝑥 = 𝐴