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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 )