Metamath Proof Explorer

Theorem ringmnd

Description: A ring is a monoid under addition. (Contributed by Mario Carneiro, 7-Jan-2015)

Ref Expression
Assertion ringmnd 
|- ( R e. Ring -> R e. Mnd )

Proof

Step Hyp Ref Expression
1 ringgrp 
 |-  ( R e. Ring -> R e. Grp )
2 grpmnd 
 |-  ( R e. Grp -> R e. Mnd )
3 1 2 syl 
 |-  ( R e. Ring -> R e. Mnd )