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Definition df-fi 6968
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 6971). (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 6967 . 2 class fi
2 vx . . 3 setvar 𝑥
3 cvv 2738 . . 3 class V
4 vz . . . . . . 7 setvar 𝑧
54cv 1352 . . . . . 6 class 𝑧
6 vy . . . . . . . 8 setvar 𝑦
76cv 1352 . . . . . . 7 class 𝑦
87cint 3845 . . . . . 6 class 𝑦
95, 8wceq 1353 . . . . 5 wff 𝑧 = 𝑦
102cv 1352 . . . . . . 7 class 𝑥
1110cpw 3576 . . . . . 6 class 𝒫 𝑥
12 cfn 6740 . . . . . 6 class Fin
1311, 12cin 3129 . . . . 5 class (𝒫 𝑥 ∩ Fin)
149, 6, 13wrex 2456 . . . 4 wff 𝑦 ∈ (𝒫 𝑥 ∩ Fin)𝑧 = 𝑦
1514, 4cab 2163 . . 3 class {𝑧 ∣ ∃𝑦 ∈ (𝒫 𝑥 ∩ Fin)𝑧 = 𝑦}
162, 3, 15cmpt 4065 . 2 class (𝑥 ∈ V ↦ {𝑧 ∣ ∃𝑦 ∈ (𝒫 𝑥 ∩ Fin)𝑧 = 𝑦})
171, 16wceq 1353 1 wff fi = (𝑥 ∈ V ↦ {𝑧 ∣ ∃𝑦 ∈ (𝒫 𝑥 ∩ Fin)𝑧 = 𝑦})
Colors of variables: wff set class
This definition is referenced by:  fival  6969
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