Metamath Proof Explorer

Theorem ablcmn

Description: An Abelian group is a commutative monoid. (Contributed by Mario Carneiro, 6-Jan-2015)

Ref Expression
Assertion ablcmn 
|- ( G e. Abel -> G e. CMnd )

Proof

Step Hyp Ref Expression
1 isabl 
 |-  ( G e. Abel <-> ( G e. Grp /\ G e. CMnd ) )
2 1 simprbi 
 |-  ( G e. Abel -> G e. CMnd )