Theorem bj-pr1val

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

	Ref	Expression
Assertion	bj-pr1val	|- pr1 ( { A } X. tag B ) = if ( A = (/) , B , (/) )

Proof

Step	Hyp	Ref	Expression
1		df-bj-pr1	|- pr1 ( { A } X. tag B ) = ( (/) Proj ( { A } X. tag B ) )
2		0ex	|- (/) e. _V
3		bj-projval	|- ( (/) e. _V -> ( (/) Proj ( { A } X. tag B ) ) = if ( A = (/) , B , (/) ) )
4	2 3	ax-mp	|- ( (/) Proj ( { A } X. tag B ) ) = if ( A = (/) , B , (/) )
5	1 4	eqtri	|- pr1 ( { A } X. tag B ) = if ( A = (/) , B , (/) )