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Definition df-z 10321
Description: Define the set of integers, which are the positive and negative natural numbers together with zero. Definition of integers in [Apostol] p. 22. The letter Z abbreviates the German word Zahlen meaning "numbers." (Contributed by NM, 8-Jan-2002.)
Assertion
Ref Expression
df-z ℤ = {𝑛 ∈ ℝ ∣ (𝑛 = 0 ∨ 𝑛 ∈ ℕ ∨ -𝑛 ∈ ℕ)}

Detailed syntax breakdown of Definition df-z
StepHypRef Expression
1 cz 10320 . 2 class
2 vn . . . . . 6 set 𝑛
32cv 1653 . . . . 5 class 𝑛
4 cc0 9028 . . . . 5 class 0
53, 4wceq 1654 . . . 4 wff 𝑛 = 0
6 cn 10038 . . . . 5 class
73, 6wcel 1728 . . . 4 wff 𝑛 ∈ ℕ
83cneg 9330 . . . . 5 class -𝑛
98, 6wcel 1728 . . . 4 wff -𝑛 ∈ ℕ
105, 7, 9w3o 936 . . 3 wff (𝑛 = 0 ∨ 𝑛 ∈ ℕ ∨ -𝑛 ∈ ℕ)
11 cr 9027 . . 3 class
1210, 2, 11crab 2716 . 2 class {𝑛 ∈ ℝ ∣ (𝑛 = 0 ∨ 𝑛 ∈ ℕ ∨ -𝑛 ∈ ℕ)}
131, 12wceq 1654 1 wff ℤ = {𝑛 ∈ ℝ ∣ (𝑛 = 0 ∨ 𝑛 ∈ ℕ ∨ -𝑛 ∈ ℕ)}
Colors of variables: wff set class
This definition is referenced by:  elz  10322
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