Definition df-z 4564

Description: Define the set of integers. Definition of integers in [Apostol] p. 22.

Assertion

Ref	Expression
df-z	⊢ ℤ = {x ∈ ℝ∣(x = 0 ∨ x ∈ ℕ ∨ -x ∈ ℕ)}

Detailed syntax breakdown of Definition df-z

Step	Hyp	Ref	Expression
1		cz 4095	. 2 class ℤ
2		vx	. . . . . 6 set x
3	2	cv 1089	. . . . 5 class x
4	lnbsp;	cc0 4028	. . . . 5 class 0
5	3, 4	wceq 1091	. . . 4 wff x = 0
6		cn 4093	. . . . 5 class ℕ
7	3, 6	wcel 1092	. . . 4 wff x ∈ ℕ
8	3	cneg 4090	. . . . 5 class -x
9	8, 6	wcel 1092	. . . 4 wff -x ∈ ℕ
10	5, 7, 9	w3o 580	. . 3 wff (x = 0 ∨ x ∈ ℕ ∨ -x ∈ ℕ)
11		cr 4027	. . 3 class ℝ
12	10, 2, 11	crab 1204	. 2 class {x ∈ ℝ∣(x = 0 ∨ x ∈ ℕ ∨ -x ∈ ℕ)}
13	1, 12	wceq 1091	1 wff ℤ = {x ∈ ℝ∣(x = 0 ∨ x ∈ ℕ ∨ -x ∈ ℕ)}

This definition is referenced by:  elz 4565

metamath.org