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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 19630 | . 2 ⊢ (𝑅 ∈ Ring → 𝑅 ∈ Abel) | |
2 | ablcmn 19209 | . 2 ⊢ (𝑅 ∈ Abel → 𝑅 ∈ CMnd) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝑅 ∈ Ring → 𝑅 ∈ CMnd) |
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