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 e. ( M ... N ) -> M <_ N ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | elfzuz2 | |- ( K e. ( M ... N ) -> N e. ( ZZ>= ` M ) ) |
|
| 2 | eluzle | |- ( N e. ( ZZ>= ` M ) -> M <_ N ) |
|
| 3 | 1 2 | syl | |- ( K e. ( M ... N ) -> M <_ N ) |