Definition df-fi 7167

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 7170). (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 7166	. 2 class fi
2		vx	. . 3 setvar x
3		cvv 2802	. . 3 class _V
4		vz	. . . . . . 7 setvar z
5	4	cv 1396	. . . . . 6 class z
6		vy	. . . . . . . 8 setvar y
7	6	cv 1396	. . . . . . 7 class y
8	7	cint 3928	. . . . . 6 class |^| y
9	5, 8	wceq 1397	. . . . 5 wff z = |^| y
10	2	cv 1396	. . . . . . 7 class x
11	10	cpw 3652	. . . . . 6 class ~P x
12		cfn 6908	. . . . . 6 class Fin
13	11, 12	cin 3199	. . . . 5 class ( ~P x i^i Fin )
14	9, 6, 13	wrex 2511	. . . 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 4150	. 2 class ( x e. _V |-> { z | E. y e. ( ~P x i^i Fin ) z = |^| y } )
17	1, 16	wceq 1397	1 wff fi = ( x e. _V |-> { z | E. y e. ( ~P x i^i Fin ) z = |^| y } )

This definition is referenced by:  fival  7168