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Definition df-fi 8872
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 8875). (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 8871 . 2 class fi
2 vx . . 3 setvar 𝑥
3 cvv 3480 . . 3 class V
4 vz . . . . . . 7 setvar 𝑧
54cv 1537 . . . . . 6 class 𝑧
6 vy . . . . . . . 8 setvar 𝑦
76cv 1537 . . . . . . 7 class 𝑦
87cint 4862 . . . . . 6 class 𝑦
95, 8wceq 1538 . . . . 5 wff 𝑧 = 𝑦
102cv 1537 . . . . . . 7 class 𝑥
1110cpw 4522 . . . . . 6 class 𝒫 𝑥
12 cfn 8505 . . . . . 6 class Fin
1311, 12cin 3918 . . . . 5 class (𝒫 𝑥 ∩ Fin)
149, 6, 13wrex 3134 . . . 4 wff 𝑦 ∈ (𝒫 𝑥 ∩ Fin)𝑧 = 𝑦
1514, 4cab 2802 . . 3 class {𝑧 ∣ ∃𝑦 ∈ (𝒫 𝑥 ∩ Fin)𝑧 = 𝑦}
162, 3, 15cmpt 5132 . 2 class (𝑥 ∈ V ↦ {𝑧 ∣ ∃𝑦 ∈ (𝒫 𝑥 ∩ Fin)𝑧 = 𝑦})
171, 16wceq 1538 1 wff fi = (𝑥 ∈ V ↦ {𝑧 ∣ ∃𝑦 ∈ (𝒫 𝑥 ∩ Fin)𝑧 = 𝑦})
Colors of variables: wff setvar class
This definition is referenced by:  fival  8873
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