Definition df-fi 6946

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 6949). (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 6945	. 2 class fi
2		vx	. . 3 setvar x
3		cvv 2730	. . 3 class _V
4		vz	. . . . . . 7 setvar z
5	4	cv 1347	. . . . . 6 class z
6		vy	. . . . . . . 8 setvar y
7	6	cv 1347	. . . . . . 7 class y
8	7	cint 3831	. . . . . 6 class |^| y
9	5, 8	wceq 1348	. . . . 5 wff z = |^| y
10	2	cv 1347	. . . . . . 7 class x
11	10	cpw 3566	. . . . . 6 class ~P x
12		cfn 6718	. . . . . 6 class Fin
13	11, 12	cin 3120	. . . . 5 class ( ~P x i^i Fin )
14	9, 6, 13	wrex 2449	. . . 4 wff E. y e. ( ~P x i^i Fin ) z = |^| y
15	14, 4	cab 2156	. . 3 class { z | E. y e. ( ~P x i^i Fin ) z = |^| y }
16	2, 3, 15	cmpt 4050	. 2 class ( x e. _V |-> { z | E. y e. ( ~P x i^i Fin ) z = |^| y } )
17	1, 16	wceq 1348	1 wff fi = ( x e. _V |-> { z | E. y e. ( ~P x i^i Fin ) z = |^| y } )

This definition is referenced by:  fival  6947