Definition df-zring 21475

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 21474	. 2 class ℤring
2		ccnfld 21381	. . 3 class ℂfld
3		cz 12610	. . 3 class ℤ
4		cress 17273	. . 3 class ↾s
5	2, 3, 4	co 7430	. 2 class (ℂfld ↾s ℤ)
6	1, 5	wceq 1536	1 wff ℤring = (ℂfld ↾s ℤ)

This definition is referenced by:  zringcrng  21476  zringbas  21481  zringplusg  21482  zringsub  21483  zringmulg  21484  zringmulr  21485  zring0  21486  zring1  21487  zringlpirlem1  21490  zringunit  21494  zringcyg  21497  zringsubgval  21498  zringmpg  21499  prmirred  21502  zndvds  21585  zringnrg  24823  zlmclm  25158  zclmncvs  25195  lgseisenlem4  27436  gsumzrsum  33044  zringnm  33918