Metamath Proof Explorer


Theorem ringcmnd

Description: A ring is a commutative monoid. (Contributed by SN, 1-Jun-2024)

Ref Expression
Hypothesis ringabld.1 ⊢ ( 𝜑 → 𝑅 ∈ Ring )
Assertion ringcmnd ( 𝜑 → 𝑅 ∈ CMnd )

Proof

Step Hyp Ref Expression
1 ringabld.1 ⊢ ( 𝜑 → 𝑅 ∈ Ring )
2 1 ringabld ⊢ ( 𝜑 → 𝑅 ∈ Abel )
3 2 ablcmnd ⊢ ( 𝜑 → 𝑅 ∈ CMnd )