Theorem bj-projex

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

	Ref	Expression
Assertion	bj-projex	|- ( B e. V -> ( A Proj B ) e. _V )

Proof

Step	Hyp	Ref	Expression
1		df-bj-proj	|- ( A Proj B ) = { x | { x } e. ( B " { A } ) }
2		bj-clex	|- ( B e. V -> { x | { x } e. ( B " { A } ) } e. _V )
3	1 2	eqeltrid	|- ( B e. V -> ( A Proj B ) e. _V )