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Definition df-fi 8864
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 8867). (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 8863 . 2 class fi
2 vx . . 3 setvar 𝑥
3 cvv 3495 . . 3 class V
4 vz . . . . . . 7 setvar 𝑧
54cv 1527 . . . . . 6 class 𝑧
6 vy . . . . . . . 8 setvar 𝑦
76cv 1527 . . . . . . 7 class 𝑦
87cint 4869 . . . . . 6 class 𝑦
95, 8wceq 1528 . . . . 5 wff 𝑧 = 𝑦
102cv 1527 . . . . . . 7 class 𝑥
1110cpw 4537 . . . . . 6 class 𝒫 𝑥
12 cfn 8498 . . . . . 6 class Fin
1311, 12cin 3934 . . . . 5 class (𝒫 𝑥 ∩ Fin)
149, 6, 13wrex 3139 . . . 4 wff 𝑦 ∈ (𝒫 𝑥 ∩ Fin)𝑧 = 𝑦
1514, 4cab 2799 . . 3 class {𝑧 ∣ ∃𝑦 ∈ (𝒫 𝑥 ∩ Fin)𝑧 = 𝑦}
162, 3, 15cmpt 5138 . 2 class (𝑥 ∈ V ↦ {𝑧 ∣ ∃𝑦 ∈ (𝒫 𝑥 ∩ Fin)𝑧 = 𝑦})
171, 16wceq 1528 1 wff fi = (𝑥 ∈ V ↦ {𝑧 ∣ ∃𝑦 ∈ (𝒫 𝑥 ∩ Fin)𝑧 = 𝑦})
Colors of variables: wff setvar class
This definition is referenced by:  fival  8865
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