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| Description: Implication of membership in an upper set of integers. (Contributed by NM, 6-Sep-2005.) | 
| Ref | Expression | 
|---|---|
| eluzle | ⊢ (𝑁 ∈ (ℤ≥‘𝑀) → 𝑀 ≤ 𝑁) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | eluz2 12884 | . 2 ⊢ (𝑁 ∈ (ℤ≥‘𝑀) ↔ (𝑀 ∈ ℤ ∧ 𝑁 ∈ ℤ ∧ 𝑀 ≤ 𝑁)) | |
| 2 | 1 | simp3bi 1148 | 1 ⊢ (𝑁 ∈ (ℤ≥‘𝑀) → 𝑀 ≤ 𝑁) | 
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