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| Mirrors > Home > MPE Home > Th. List > elfzonn0 | Structured version Visualization version GIF version | ||
| Description: A member of a half-open range of nonnegative integers is a nonnegative integer. (Contributed by Alexander van der Vekens, 21-May-2018.) | 
| Ref | Expression | 
|---|---|
| elfzonn0 | ⊢ (𝐾 ∈ (0..^𝑁) → 𝐾 ∈ ℕ0) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | elfzouz 13704 | . 2 ⊢ (𝐾 ∈ (0..^𝑁) → 𝐾 ∈ (ℤ≥‘0)) | |
| 2 | elnn0uz 12924 | . 2 ⊢ (𝐾 ∈ ℕ0 ↔ 𝐾 ∈ (ℤ≥‘0)) | |
| 3 | 1, 2 | sylibr 234 | 1 ⊢ (𝐾 ∈ (0..^𝑁) → 𝐾 ∈ ℕ0) | 
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