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| Mirrors > Home > MPE Home > Th. List > crngring | Structured version Visualization version GIF version | ||
| Description: A commutative ring is a ring. (Contributed by Mario Carneiro, 7-Jan-2015.) |
| Ref | Expression |
|---|---|
| crngring | ⊢ (𝑅 ∈ CRing → 𝑅 ∈ Ring) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | eqid 2737 | . . 3 ⊢ (mulGrp‘𝑅) = (mulGrp‘𝑅) | |
| 2 | 1 | iscrng 20237 | . 2 ⊢ (𝑅 ∈ CRing ↔ (𝑅 ∈ Ring ∧ (mulGrp‘𝑅) ∈ CMnd)) |
| 3 | 2 | simplbi 497 | 1 ⊢ (𝑅 ∈ CRing → 𝑅 ∈ Ring) |
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