Definition df-fi 6906

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 6909). (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 6905	. 2 class fi
2		vx	. . 3 setvar x
3		cvv 2712	. . 3 class _V
4		vz	. . . . . . 7 setvar z
5	4	cv 1334	. . . . . 6 class z
6		vy	. . . . . . . 8 setvar y
7	6	cv 1334	. . . . . . 7 class y
8	7	cint 3807	. . . . . 6 class |^| y
9	5, 8	wceq 1335	. . . . 5 wff z = |^| y
10	2	cv 1334	. . . . . . 7 class x
11	10	cpw 3543	. . . . . 6 class ~P x
12		cfn 6678	. . . . . 6 class Fin
13	11, 12	cin 3101	. . . . 5 class ( ~P x i^i Fin )
14	9, 6, 13	wrex 2436	. . . 4 wff E. y e. ( ~P x i^i Fin ) z = |^| y
15	14, 4	cab 2143	. . 3 class { z | E. y e. ( ~P x i^i Fin ) z = |^| y }
16	2, 3, 15	cmpt 4025	. 2 class ( x e. _V |-> { z | E. y e. ( ~P x i^i Fin ) z = |^| y } )
17	1, 16	wceq 1335	1 wff fi = ( x e. _V |-> { z | E. y e. ( ~P x i^i Fin ) z = |^| y } )

This definition is referenced by:  fival  6907