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Definition df-uz 8474
 Description: Define a function whose value at 𝑗 is the semi-infinite set of contiguous integers starting at 𝑗, which we will also call the upper integers starting at 𝑗. Read "ℤ≥‘𝑀 " as "the set of integers greater than or equal to 𝑀." See uzval 8475 for its value, uzssz 8492 for its relationship to ℤ, nnuz 8508 and nn0uz 8507 for its relationships to ℕ and ℕ0, and eluz1 8477 and eluz2 8479 for its membership relations. (Contributed by NM, 5-Sep-2005.)
Assertion
Ref Expression
df-uz = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗𝑘})
Distinct variable group:   𝑗,𝑘

Detailed syntax breakdown of Definition df-uz
StepHypRef Expression
1 cuz 8473 . 2 class
2 vj . . 3 setvar 𝑗
3 cz 8245 . . 3 class
42cv 1242 . . . . 5 class 𝑗
5 vk . . . . . 6 setvar 𝑘
65cv 1242 . . . . 5 class 𝑘
7 cle 7061 . . . . 5 class
84, 6, 7wbr 3764 . . . 4 wff 𝑗𝑘
98, 5, 3crab 2310 . . 3 class {𝑘 ∈ ℤ ∣ 𝑗𝑘}
102, 3, 9cmpt 3818 . 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗𝑘})
111, 10wceq 1243 1 wff = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗𝑘})
 Colors of variables: wff set class This definition is referenced by:  uzval  8475  uzf  8476
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