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Definition df-fi 8676
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 8679). (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 8675 . 2 class fi
2 vx . . 3 setvar 𝑥
3 cvv 3417 . . 3 class V
4 vz . . . . . . 7 setvar 𝑧
54cv 1507 . . . . . 6 class 𝑧
6 vy . . . . . . . 8 setvar 𝑦
76cv 1507 . . . . . . 7 class 𝑦
87cint 4754 . . . . . 6 class 𝑦
95, 8wceq 1508 . . . . 5 wff 𝑧 = 𝑦
102cv 1507 . . . . . . 7 class 𝑥
1110cpw 4425 . . . . . 6 class 𝒫 𝑥
12 cfn 8312 . . . . . 6 class Fin
1311, 12cin 3830 . . . . 5 class (𝒫 𝑥 ∩ Fin)
149, 6, 13wrex 3091 . . . 4 wff 𝑦 ∈ (𝒫 𝑥 ∩ Fin)𝑧 = 𝑦
1514, 4cab 2760 . . 3 class {𝑧 ∣ ∃𝑦 ∈ (𝒫 𝑥 ∩ Fin)𝑧 = 𝑦}
162, 3, 15cmpt 5013 . 2 class (𝑥 ∈ V ↦ {𝑧 ∣ ∃𝑦 ∈ (𝒫 𝑥 ∩ Fin)𝑧 = 𝑦})
171, 16wceq 1508 1 wff fi = (𝑥 ∈ V ↦ {𝑧 ∣ ∃𝑦 ∈ (𝒫 𝑥 ∩ Fin)𝑧 = 𝑦})
Colors of variables: wff setvar class
This definition is referenced by:  fival  8677
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