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Definition df-fi 6857
 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 6860). (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 6856 . 2 class fi
2 vx . . 3 setvar 𝑥
3 cvv 2686 . . 3 class V
4 vz . . . . . . 7 setvar 𝑧
54cv 1330 . . . . . 6 class 𝑧
6 vy . . . . . . . 8 setvar 𝑦
76cv 1330 . . . . . . 7 class 𝑦
87cint 3771 . . . . . 6 class 𝑦
95, 8wceq 1331 . . . . 5 wff 𝑧 = 𝑦
102cv 1330 . . . . . . 7 class 𝑥
1110cpw 3510 . . . . . 6 class 𝒫 𝑥
12 cfn 6634 . . . . . 6 class Fin
1311, 12cin 3070 . . . . 5 class (𝒫 𝑥 ∩ Fin)
149, 6, 13wrex 2417 . . . 4 wff 𝑦 ∈ (𝒫 𝑥 ∩ Fin)𝑧 = 𝑦
1514, 4cab 2125 . . 3 class {𝑧 ∣ ∃𝑦 ∈ (𝒫 𝑥 ∩ Fin)𝑧 = 𝑦}
162, 3, 15cmpt 3989 . 2 class (𝑥 ∈ V ↦ {𝑧 ∣ ∃𝑦 ∈ (𝒫 𝑥 ∩ Fin)𝑧 = 𝑦})
171, 16wceq 1331 1 wff fi = (𝑥 ∈ V ↦ {𝑧 ∣ ∃𝑦 ∈ (𝒫 𝑥 ∩ Fin)𝑧 = 𝑦})
 Colors of variables: wff set class This definition is referenced by:  fival  6858
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