Theorem zringrng

Description: The ring of integers is a non-unital ring. (Contributed by AV, 17-Mar-2025)

	Ref	Expression
Assertion	zringrng	$$⊢{\mathbb{Z}}_{\mathrm{ring}}\in \mathrm{Rng}$$

Proof

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