Definition df-fi 6857

Description: Function whose value is the class of finite intersections of the elements of the argument. Note that the empty intersection being the universal class, hence a proper class, it cannot be an element of that class. Therefore, the function value is the class of nonempty finite intersections of elements of the argument (see elfi2 6860). (Contributed by FL, 27-Apr-2008.)

Assertion

Ref	Expression
df-fi	|- fi = ( x e. _V |-> { z | E. y e. ( ~P x i^i Fin ) z = |^| y } )

Distinct variable group:   x, y, z

Detailed syntax breakdown of Definition df-fi

Step	Hyp	Ref	Expression
1		cfi 6856	. 2 class fi
2		vx	. . 3 setvar x
3		cvv 2686	. . 3 class _V
4		vz	. . . . . . 7 setvar z
5	4	cv 1330	. . . . . 6 class z
6		vy	. . . . . . . 8 setvar y
7	6	cv 1330	. . . . . . 7 class y
8	7	cint 3771	. . . . . 6 class |^| y
9	5, 8	wceq 1331	. . . . 5 wff z = |^| y
10	2	cv 1330	. . . . . . 7 class x
11	10	cpw 3510	. . . . . 6 class ~P x
12		cfn 6634	. . . . . 6 class Fin
13	11, 12	cin 3070	. . . . 5 class ( ~P x i^i Fin )
14	9, 6, 13	wrex 2417	. . . 4 wff E. y e. ( ~P x i^i Fin ) z = |^| y
15	14, 4	cab 2125	. . 3 class { z | E. y e. ( ~P x i^i Fin ) z = |^| y }
16	2, 3, 15	cmpt 3989	. 2 class ( x e. _V |-> { z | E. y e. ( ~P x i^i Fin ) z = |^| y } )
17	1, 16	wceq 1331	1 wff fi = ( x e. _V |-> { z | E. y e. ( ~P x i^i Fin ) z = |^| y } )

This definition is referenced by:  fival  6858