Theorem bj-pr2val

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

	Ref	Expression
Assertion	bj-pr2val	|- pr2 ( { A } X. tag B ) = if ( A = 1o , B , (/) )

Proof

Step	Hyp	Ref	Expression
1		df-bj-pr2	|- pr2 ( { A } X. tag B ) = ( 1o Proj ( { A } X. tag B ) )
2		1oex	|- 1o e. _V
3		bj-projval	|- ( 1o e. _V -> ( 1o Proj ( { A } X. tag B ) ) = if ( A = 1o , B , (/) ) )
4	2 3	ax-mp	|- ( 1o Proj ( { A } X. tag B ) ) = if ( A = 1o , B , (/) )
5	1 4	eqtri	|- pr2 ( { A } X. tag B ) = if ( A = 1o , B , (/) )