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∈Abel→G∈CMnd

Proof

Step Hyp Ref Expression
1 isabl ⊢G∈Abel↔G∈Grp∧G∈CMnd
2 1 simprbi ⊢G∈Abel→G∈CMnd