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Definition df-fi 7070
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 7073). (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 7069 . 2 class fi
2 vx . . 3 setvar 𝑥
3 cvv 2771 . . 3 class V
4 vz . . . . . . 7 setvar 𝑧
54cv 1371 . . . . . 6 class 𝑧
6 vy . . . . . . . 8 setvar 𝑦
76cv 1371 . . . . . . 7 class 𝑦
87cint 3884 . . . . . 6 class 𝑦
95, 8wceq 1372 . . . . 5 wff 𝑧 = 𝑦
102cv 1371 . . . . . . 7 class 𝑥
1110cpw 3615 . . . . . 6 class 𝒫 𝑥
12 cfn 6826 . . . . . 6 class Fin
1311, 12cin 3164 . . . . 5 class (𝒫 𝑥 ∩ Fin)
149, 6, 13wrex 2484 . . . 4 wff 𝑦 ∈ (𝒫 𝑥 ∩ Fin)𝑧 = 𝑦
1514, 4cab 2190 . . 3 class {𝑧 ∣ ∃𝑦 ∈ (𝒫 𝑥 ∩ Fin)𝑧 = 𝑦}
162, 3, 15cmpt 4104 . 2 class (𝑥 ∈ V ↦ {𝑧 ∣ ∃𝑦 ∈ (𝒫 𝑥 ∩ Fin)𝑧 = 𝑦})
171, 16wceq 1372 1 wff fi = (𝑥 ∈ V ↦ {𝑧 ∣ ∃𝑦 ∈ (𝒫 𝑥 ∩ Fin)𝑧 = 𝑦})
Colors of variables: wff set class
This definition is referenced by:  fival  7071
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