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| Mirrors > Home > MPE Home > Th. List > ringcmn | Structured version Visualization version GIF version | ||
| Description: A ring is a commutative monoid. (Contributed by Mario Carneiro, 7-Jan-2015.) |
| Ref | Expression |
|---|---|
| ringcmn | ⊢ (𝑅 ∈ Ring → 𝑅 ∈ CMnd) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ringabl 20278 | . 2 ⊢ (𝑅 ∈ Ring → 𝑅 ∈ Abel) | |
| 2 | ablcmn 19805 | . 2 ⊢ (𝑅 ∈ Abel → 𝑅 ∈ CMnd) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝑅 ∈ Ring → 𝑅 ∈ CMnd) |
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