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Metamath Proof Explorer

Theorem ablcmnd

Description: An Abelian group is a commutative monoid. (Contributed by SN, 1-Jun-2024)

Ref Expression
Hypothesis ablcmnd.1 ⊢ ( 𝜑 → 𝐺 ∈ Abel )
Assertion ablcmnd ( 𝜑 → 𝐺 ∈ CMnd )

Proof

Step Hyp Ref Expression
1 ablcmnd.1 ⊢ ( 𝜑 → 𝐺 ∈ Abel )
2 ablcmn ⊢ ( 𝐺 ∈ Abel → 𝐺 ∈ CMnd )
3 1 2 syl ⊢ ( 𝜑 → 𝐺 ∈ CMnd )