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