ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  df-z Structured version   GIF version

Definition df-z 8002
Description: Define the set of integers, which are the positive and negative integers 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)}

Detailed syntax breakdown of Definition df-z
StepHypRef Expression
1 cz 8001 . 2 class
2 vn . . . . . 6 setvar 𝑛
32cv 1241 . . . . 5 class 𝑛
4 cc0 6691 . . . . 5 class 0
53, 4wceq 1242 . . . 4 wff 𝑛 = 0
6 cn 7675 . . . . 5 class
73, 6wcel 1390 . . . 4 wff 𝑛
83cneg 6960 . . . . 5 class -𝑛
98, 6wcel 1390 . . . 4 wff -𝑛
105, 7, 9w3o 883 . . 3 wff (𝑛 = 0 𝑛 -𝑛 ℕ)
11 cr 6690 . . 3 class
1210, 2, 11crab 2304 . 2 class {𝑛 ℝ ∣ (𝑛 = 0 𝑛 -𝑛 ℕ)}
131, 12wceq 1242 1 wff ℤ = {𝑛 ℝ ∣ (𝑛 = 0 𝑛 -𝑛 ℕ)}
Colors of variables: wff set class
This definition is referenced by:  elz  8003
  Copyright terms: Public domain W3C validator