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Definition df-z 9957
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  |-  ZZ  =  { n  e.  RR  |  ( n  =  0  \/  n  e.  NN  \/  -u n  e.  NN ) }

Detailed syntax breakdown of Definition df-z
StepHypRef Expression
1 cz 9956 . 2  class  ZZ
2 vn . . . . . 6  set  n
32cv 1618 . . . . 5  class  n
4 cc0 8670 . . . . 5  class  0
53, 4wceq 1619 . . . 4  wff  n  =  0
6 cn 9679 . . . . 5  class  NN
73, 6wcel 1621 . . . 4  wff  n  e.  NN
83cneg 8971 . . . . 5  class  -u n
98, 6wcel 1621 . . . 4  wff  -u n  e.  NN
105, 7, 9w3o 938 . . 3  wff  ( n  =  0  \/  n  e.  NN  \/  -u n  e.  NN )
11 cr 8669 . . 3  class  RR
1210, 2, 11crab 2519 . 2  class  { n  e.  RR  |  ( n  =  0  \/  n  e.  NN  \/  -u n  e.  NN ) }
131, 12wceq 1619 1  wff  ZZ  =  { n  e.  RR  |  ( n  =  0  \/  n  e.  NN  \/  -u n  e.  NN ) }
Colors of variables: wff set class
This definition is referenced by:  elz  9958
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