Theorem bj-pr1ex

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

	Ref	Expression
Assertion	bj-pr1ex	⊢ ( 𝐴 ∈ 𝑉 → pr1 𝐴 ∈ V )

Proof

Step	Hyp	Ref	Expression
1		df-bj-pr1	⊢ pr1 𝐴 = ( ∅ Proj 𝐴 )
2		bj-projex	⊢ ( 𝐴 ∈ 𝑉 → ( ∅ Proj 𝐴 ) ∈ V )
3	1 2	eqeltrid	⊢ ( 𝐴 ∈ 𝑉 → pr1 𝐴 ∈ V )