This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

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 e. Rng -> R e. Grp )

Proof

Step Hyp Ref Expression
1 rngabl 
 |-  ( R e. Rng -> R e. Abel )
2 1 ablgrpd 
 |-  ( R e. Rng -> R e. Grp )