Theorem rnggrp

Description: A non-unital ring is a (additive) group. (Contributed by AV, 16-Feb-2025)

	Ref	Expression
Assertion	rnggrp	$$⊢R\in \mathrm{Rng}\to R\in \mathrm{Grp}$$

Proof

Step	Hyp	Ref	Expression
1		rngabl	$$⊢R\in \mathrm{Rng}\to R\in \mathrm{Abel}$$
2	1	ablgrpd	$$⊢R\in \mathrm{Rng}\to R\in \mathrm{Grp}$$