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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 12343 | . 2 ⊢ (𝐾 ∈ (0..^𝑁) → 𝐾 ∈ (ℤ≥‘0)) | |
2 | elnn0uz 11601 | . 2 ⊢ (𝐾 ∈ ℕ0 ↔ 𝐾 ∈ (ℤ≥‘0)) | |
3 | 1, 2 | sylibr 223 | 1 ⊢ (𝐾 ∈ (0..^𝑁) → 𝐾 ∈ ℕ0) |
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