Theorem bj-projex

Description: Sethood of the class projection. (Contributed by BJ, 6-Apr-2019)

	Ref	Expression
Assertion	bj-projex	⊢ ( 𝐵 ∈ 𝑉 → ( 𝐴 Proj 𝐵 ) ∈ V )

Proof

Step	Hyp	Ref	Expression
1		df-bj-proj	⊢ ( 𝐴 Proj 𝐵 ) = { 𝑥 ∣ { 𝑥 } ∈ ( 𝐵 “ { 𝐴 } ) }
2		bj-clexab	⊢ ( 𝐵 ∈ 𝑉 → { 𝑥 ∣ { 𝑥 } ∈ ( 𝐵 “ { 𝐴 } ) } ∈ V )
3	1 2	eqeltrid	⊢ ( 𝐵 ∈ 𝑉 → ( 𝐴 Proj 𝐵 ) ∈ V )