Description: Membership in a finite set of sequential integer implies the lower bound is an integer. (Contributed by NM, 6-Sep-2005) (Revised by Mario Carneiro, 28-Apr-2015)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | elfzel1 | |- ( K e. ( M ... N ) -> M e. ZZ ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | elfzuz | |- ( K e. ( M ... N ) -> K e. ( ZZ>= ` M ) ) |
|
| 2 | eluzel2 | |- ( K e. ( ZZ>= ` M ) -> M e. ZZ ) |
|
| 3 | 1 2 | syl | |- ( K e. ( M ... N ) -> M e. ZZ ) |