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Metamath Proof Explorer

Theorem rnggrp

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

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

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