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 ∈ 𝑉
Assertion	bj-issetiv	⊢ ∃ 𝑥 𝑥 = 𝐴

Proof

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