Description: Membership in a finite set of sequential integer implies the bounds are comparable. (Contributed by NM, 18-Sep-2005) (Revised by Mario Carneiro, 28-Apr-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | elfzle3 | ⊢ ( 𝐾 ∈ ( 𝑀 ... 𝑁 ) → 𝑀 ≤ 𝑁 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elfzuz2 | ⊢ ( 𝐾 ∈ ( 𝑀 ... 𝑁 ) → 𝑁 ∈ ( ℤ≥ ‘ 𝑀 ) ) | |
2 | eluzle | ⊢ ( 𝑁 ∈ ( ℤ≥ ‘ 𝑀 ) → 𝑀 ≤ 𝑁 ) | |
3 | 1 2 | syl | ⊢ ( 𝐾 ∈ ( 𝑀 ... 𝑁 ) → 𝑀 ≤ 𝑁 ) |