Definition df-bj-proj

Description: Definition of the class projection corresponding to tagged tuples. The expression ( A Proj B ) denotes the projection on the A^th component. (Contributed by BJ, 6-Apr-2019) (New usage is discouraged.)

	Ref	Expression
Assertion	df-bj-proj	⊢ ( 𝐴 Proj 𝐵 ) = { 𝑥 ∣ { 𝑥 } ∈ ( 𝐵 “ { 𝐴 } ) }

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cA	⊢ 𝐴
1		cB	⊢ 𝐵
2	0 1	bj-cproj	⊢ ( 𝐴 Proj 𝐵 )
3		vx	⊢ 𝑥
4	3	cv	⊢ 𝑥
5	4	csn	⊢ { 𝑥 }
6	0	csn	⊢ { 𝐴 }
7	1 6	cima	⊢ ( 𝐵 “ { 𝐴 } )
8	5 7	wcel	⊢ { 𝑥 } ∈ ( 𝐵 “ { 𝐴 } )
9	8 3	cab	⊢ { 𝑥 ∣ { 𝑥 } ∈ ( 𝐵 “ { 𝐴 } ) }
10	2 9	wceq	⊢ ( 𝐴 Proj 𝐵 ) = { 𝑥 ∣ { 𝑥 } ∈ ( 𝐵 “ { 𝐴 } ) }