Theorem rnggrp

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

	Ref	Expression
Assertion	rnggrp	⊢ ( 𝑅 ∈ Rng → 𝑅 ∈ Grp )

Proof

Step	Hyp	Ref	Expression
1		rngabl	⊢ ( 𝑅 ∈ Rng → 𝑅 ∈ Abel )
2	1	ablgrpd	⊢ ( 𝑅 ∈ Rng → 𝑅 ∈ Grp )