| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > elfzle2 | Structured version Visualization version GIF version | ||
| Description: A member of a finite set of sequential integer is less than or equal to the upper bound. (Contributed by NM, 6-Sep-2005.) (Revised by Mario Carneiro, 28-Apr-2015.) |
| Ref | Expression |
|---|---|
| elfzle2 | ⊢ (𝐾 ∈ (𝑀...𝑁) → 𝐾 ≤ 𝑁) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | elfzuz3 13561 | . 2 ⊢ (𝐾 ∈ (𝑀...𝑁) → 𝑁 ∈ (ℤ≥‘𝐾)) | |
| 2 | eluzle 12891 | . 2 ⊢ (𝑁 ∈ (ℤ≥‘𝐾) → 𝐾 ≤ 𝑁) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝐾 ∈ (𝑀...𝑁) → 𝐾 ≤ 𝑁) |
| Copyright terms: Public domain | W3C validator |