Description: If there is a member in a finite set of sequential integers, the upper bound is also a member of this finite set of sequential integers. (Contributed by Alexander van der Vekens, 31-May-2018)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | elfzubelfz | |- ( K e. ( M ... N ) -> N e. ( M ... N ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | elfzuz2 | |- ( K e. ( M ... N ) -> N e. ( ZZ>= ` M ) ) |
|
| 2 | eluzfz2 | |- ( N e. ( ZZ>= ` M ) -> N e. ( M ... N ) ) |
|
| 3 | 1 2 | syl | |- ( K e. ( M ... N ) -> N e. ( M ... N ) ) |