Definition df-zring 21458

Description: The (unital) ring of integers. (Contributed by Alexander van der Vekens, 9-Jun-2019.)

Assertion

Ref	Expression
df-zring	⊢ ℤring = (ℂfld ↾s ℤ)

Detailed syntax breakdown of Definition df-zring

Step	Hyp	Ref	Expression
1		czring 21457	. 2 class ℤring
2		ccnfld 21364	. . 3 class ℂfld
3		cz 12613	. . 3 class ℤ
4		cress 17274	. . 3 class ↾s
5	2, 3, 4	co 7431	. 2 class (ℂfld ↾s ℤ)
6	1, 5	wceq 1540	1 wff ℤring = (ℂfld ↾s ℤ)

This definition is referenced by:  zringcrng  21459  zringbas  21464  zringplusg  21465  zringsub  21466  zringmulg  21467  zringmulr  21468  zring0  21469  zring1  21470  zringlpirlem1  21473  zringunit  21477  zringcyg  21480  zringsubgval  21481  zringmpg  21482  prmirred  21485  zndvds  21568  zringnrg  24809  zlmclm  25145  zclmncvs  25182  lgseisenlem4  27422  gsumzrsum  33062  zringnm  33957