Definition df-fi 7256

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 7259). (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 7255	. 2 class fi
2		vx	. . 3 setvar x
3		cvv 2813	. . 3 class _V
4		vz	. . . . . . 7 setvar z
5	4	cv 1397	. . . . . 6 class z
6		vy	. . . . . . . 8 setvar y
7	6	cv 1397	. . . . . . 7 class y
8	7	cint 3949	. . . . . 6 class |^| y
9	5, 8	wceq 1398	. . . . 5 wff z = |^| y
10	2	cv 1397	. . . . . . 7 class x
11	10	cpw 3669	. . . . . 6 class ~P x
12		cfn 6975	. . . . . 6 class Fin
13	11, 12	cin 3210	. . . . 5 class ( ~P x i^i Fin )
14	9, 6, 13	wrex 2521	. . . 4 wff E. y e. ( ~P x i^i Fin ) z = |^| y
15	14, 4	cab 2218	. . 3 class { z | E. y e. ( ~P x i^i Fin ) z = |^| y }
16	2, 3, 15	cmpt 4171	. 2 class ( x e. _V |-> { z | E. y e. ( ~P x i^i Fin ) z = |^| y } )
17	1, 16	wceq 1398	1 wff fi = ( x e. _V |-> { z | E. y e. ( ~P x i^i Fin ) z = |^| y } )

This definition is referenced by:  fival  7257