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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 ∈ 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 6945 . 2 class fi
2 vx . . 3 setvar 𝑥
3 cvv 2730 . . 3 class V
4 vz . . . . . . 7 setvar 𝑧
54cv 1347 . . . . . 6 class 𝑧
6 vy . . . . . . . 8 setvar 𝑦
76cv 1347 . . . . . . 7 class 𝑦
87cint 3831 . . . . . 6 class 𝑦
95, 8wceq 1348 . . . . 5 wff 𝑧 = 𝑦
102cv 1347 . . . . . . 7 class 𝑥
1110cpw 3566 . . . . . 6 class 𝒫 𝑥
12 cfn 6718 . . . . . 6 class Fin
1311, 12cin 3120 . . . . 5 class (𝒫 𝑥 ∩ Fin)
149, 6, 13wrex 2449 . . . 4 wff 𝑦 ∈ (𝒫 𝑥 ∩ Fin)𝑧 = 𝑦
1514, 4cab 2156 . . 3 class {𝑧 ∣ ∃𝑦 ∈ (𝒫 𝑥 ∩ Fin)𝑧 = 𝑦}
162, 3, 15cmpt 4050 . 2 class (𝑥 ∈ V ↦ {𝑧 ∣ ∃𝑦 ∈ (𝒫 𝑥 ∩ Fin)𝑧 = 𝑦})
171, 16wceq 1348 1 wff fi = (𝑥 ∈ V ↦ {𝑧 ∣ ∃𝑦 ∈ (𝒫 𝑥 ∩ Fin)𝑧 = 𝑦})
Colors of variables: wff set class
This definition is referenced by:  fival  6947
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