Definition df-z 9253

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 e. RR | ( n = 0 \/ n e. NN \/ -u n e. NN ) }

Detailed syntax breakdown of Definition df-z

Step	Hyp	Ref	Expression
1		cz 9252	. 2 class ZZ
2		vn	. . . . . 6 setvar n
3	2	cv 1352	. . . . 5 class n
4		cc0 7810	. . . . 5 class 0
5	3, 4	wceq 1353	. . . 4 wff n = 0
6		cn 8918	. . . . 5 class NN
7	3, 6	wcel 2148	. . . 4 wff n e. NN
8	3	cneg 8128	. . . . 5 class -u n
9	8, 6	wcel 2148	. . . 4 wff -u n e. NN
10	5, 7, 9	w3o 977	. . 3 wff ( n = 0 \/ n e. NN \/ -u n e. NN )
11		cr 7809	. . 3 class RR
12	10, 2, 11	crab 2459	. 2 class { n e. RR | ( n = 0 \/ n e. NN \/ -u n e. NN ) }
13	1, 12	wceq 1353	1 wff ZZ = { n e. RR | ( n = 0 \/ n e. NN \/ -u n e. NN ) }

This definition is referenced by:  elz  9254