Theorem bj-pr1ex

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

	Ref	Expression
Assertion	bj-pr1ex	$$⊢A\in V\to pr1A\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		df-bj-pr1	$$⊢pr1A=\left(\varnothing ProjA\right)$$
2		bj-projex	$$⊢A\in V\to \left(\varnothing ProjA\right)\in \mathrm{V}$$
3	1 2	eqeltrid	$$⊢A\in V\to pr1A\in \mathrm{V}$$