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 )