Definition df-fi 7228

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 7231). (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 7227	. 2 class fi
2		vx	. . 3 setvar x
3		cvv 2803	. . 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 3933	. . . . . 6 class |^| y
9	5, 8	wceq 1398	. . . . 5 wff z = |^| y
10	2	cv 1397	. . . . . . 7 class x
11	10	cpw 3656	. . . . . 6 class ~P x
12		cfn 6952	. . . . . 6 class Fin
13	11, 12	cin 3200	. . . . 5 class ( ~P x i^i Fin )
14	9, 6, 13	wrex 2512	. . . 4 wff E. y e. ( ~P x i^i Fin ) z = |^| y
15	14, 4	cab 2217	. . 3 class { z | E. y e. ( ~P x i^i Fin ) z = |^| y }
16	2, 3, 15	cmpt 4155	. 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  7229