Theorem zringabl

Description: The ring of integers is an (additive) abelian group. (Contributed by AV, 13-Jun-2019)

	Ref	Expression
Assertion	zringabl	$$⊢{\mathbb{Z}}_{\mathrm{ring}}\in \mathrm{Abel}$$

Proof

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