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| Mirrors > Home > MPE Home > Th. List > fldcrngd | Structured version Visualization version GIF version | ||
| Description: A field is a commutative ring. (Contributed by SN, 23-Nov-2024.) | 
| Ref | Expression | 
|---|---|
| fldcrngd.1 | ⊢ (𝜑 → 𝑅 ∈ Field) | 
| Ref | Expression | 
|---|---|
| fldcrngd | ⊢ (𝜑 → 𝑅 ∈ CRing) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | fldcrngd.1 | . 2 ⊢ (𝜑 → 𝑅 ∈ Field) | |
| 2 | isfld 20741 | . . 3 ⊢ (𝑅 ∈ Field ↔ (𝑅 ∈ DivRing ∧ 𝑅 ∈ CRing)) | |
| 3 | 2 | simprbi 496 | . 2 ⊢ (𝑅 ∈ Field → 𝑅 ∈ CRing) | 
| 4 | 1, 3 | syl 17 | 1 ⊢ (𝜑 → 𝑅 ∈ CRing) | 
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