Theorem bj-issetiv

Description: Version of bj-isseti with a disjoint variable condition on x , V . This proof uses only df-ex , ax-gen , ax-4 and df-clel on top of propositional calculus. Prefer its use over bj-isseti when sufficient (in particular when V is substituted for _V ). (Contributed by BJ, 14-Sep-2019) (Proof modification is discouraged.)

	Ref	Expression
Hypothesis	bj-issetiv.1	$$⊢A\in V$$
Assertion	bj-issetiv	$$⊢\exists xx=A$$

Proof

Step	Hyp	Ref	Expression
1		bj-issetiv.1	$$⊢A\in V$$
2		elissetv	$$⊢A\in V\to \exists xx=A$$
3	1 2	ax-mp	$$⊢\exists xx=A$$