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

Definition df-z 8022
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  ZZ  { n  RR  |  n  0  n  NN  -u n  NN }

Detailed syntax breakdown of Definition df-z
StepHypRef Expression
1 cz 8021 . 2  ZZ
2 vn . . . . . 6  setvar  n
32cv 1241 . . . . 5  n
4 cc0 6711 . . . . 5  0
53, 4wceq 1242 . . . 4  n  0
6 cn 7695 . . . . 5  NN
73, 6wcel 1390 . . . 4  n  NN
83cneg 6980 . . . . 5  -u n
98, 6wcel 1390 . . . 4  -u n  NN
105, 7, 9w3o 883 . . 3  n  0  n  NN  -u n  NN
11 cr 6710 . . 3  RR
1210, 2, 11crab 2304 . 2  { n  RR  |  n  0  n  NN  -u n  NN }
131, 12wceq 1242 1  ZZ  { n  RR  |  n  0  n  NN  -u n  NN }
Colors of variables: wff set class
This definition is referenced by:  elz  8023
  Copyright terms: Public domain W3C validator