Theorem bj-pr2ex

Description: Sethood of the second projection. (Contributed by BJ, 6-Oct-2018)

	Ref	Expression
Assertion	bj-pr2ex	⊢ ( 𝐴 ∈ 𝑉 → pr2 𝐴 ∈ V )

Proof

Step	Hyp	Ref	Expression
1		df-bj-pr2	⊢ pr2 𝐴 = ( 1o Proj 𝐴 )
2		bj-projex	⊢ ( 𝐴 ∈ 𝑉 → ( 1o Proj 𝐴 ) ∈ V )
3	1 2	eqeltrid	⊢ ( 𝐴 ∈ 𝑉 → pr2 𝐴 ∈ V )