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Definition df-fi 8559
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 8562). (Contributed by FL, 27-Apr-2008.)
Assertion
Ref Expression
df-fi fi = (𝑥 ∈ V ↦ {𝑧 ∣ ∃𝑦 ∈ (𝒫 𝑥 ∩ Fin)𝑧 = 𝑦})
Distinct variable group:   𝑥,𝑦,𝑧

Detailed syntax breakdown of Definition df-fi
StepHypRef Expression
1 cfi 8558 . 2 class fi
2 vx . . 3 setvar 𝑥
3 cvv 3398 . . 3 class V
4 vz . . . . . . 7 setvar 𝑧
54cv 1636 . . . . . 6 class 𝑧
6 vy . . . . . . . 8 setvar 𝑦
76cv 1636 . . . . . . 7 class 𝑦
87cint 4676 . . . . . 6 class 𝑦
95, 8wceq 1637 . . . . 5 wff 𝑧 = 𝑦
102cv 1636 . . . . . . 7 class 𝑥
1110cpw 4358 . . . . . 6 class 𝒫 𝑥
12 cfn 8195 . . . . . 6 class Fin
1311, 12cin 3775 . . . . 5 class (𝒫 𝑥 ∩ Fin)
149, 6, 13wrex 3104 . . . 4 wff 𝑦 ∈ (𝒫 𝑥 ∩ Fin)𝑧 = 𝑦
1514, 4cab 2799 . . 3 class {𝑧 ∣ ∃𝑦 ∈ (𝒫 𝑥 ∩ Fin)𝑧 = 𝑦}
162, 3, 15cmpt 4930 . 2 class (𝑥 ∈ V ↦ {𝑧 ∣ ∃𝑦 ∈ (𝒫 𝑥 ∩ Fin)𝑧 = 𝑦})
171, 16wceq 1637 1 wff fi = (𝑥 ∈ V ↦ {𝑧 ∣ ∃𝑦 ∈ (𝒫 𝑥 ∩ Fin)𝑧 = 𝑦})
Colors of variables: wff setvar class
This definition is referenced by:  fival  8560
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