Theorem zringgrp

Description: The ring of integers is an (additive) group. (Contributed by AV, 10-Jun-2019)

	Ref	Expression
Assertion	zringgrp	$$⊢{\mathbb{Z}}_{\mathrm{ring}}\in \mathrm{Grp}$$

Proof

Step	Hyp	Ref	Expression
1		zringring	$$⊢{\mathbb{Z}}_{\mathrm{ring}}\in \mathrm{Ring}$$
2		ringgrp	$$⊢{\mathbb{Z}}_{\mathrm{ring}}\in \mathrm{Ring}\to {\mathbb{Z}}_{\mathrm{ring}}\in \mathrm{Grp}$$
3	1 2	ax-mp	$$⊢{\mathbb{Z}}_{\mathrm{ring}}\in \mathrm{Grp}$$