Metamath Proof Explorer

Theorem ringcmn

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

Ref Expression
Assertion ringcmn 
|- ( R e. Ring -> R e. CMnd )

Proof

Step Hyp Ref Expression
1 ringabl 
 |-  ( R e. Ring -> R e. Abel )
2 ablcmn 
 |-  ( R e. Abel -> R e. CMnd )
3 1 2 syl 
 |-  ( R e. Ring -> R e. CMnd )