Description: A member of an upper set of integers is an integer. (Contributed by Glauco Siliprandi, 23-Oct-2021)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | eluzelz2.1 | |- Z = ( ZZ>= ` M ) |
|
| Assertion | eluzelz2 | |- ( N e. Z -> N e. ZZ ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | eluzelz2.1 | |- Z = ( ZZ>= ` M ) |
|
| 2 | 1 | eleq2i | |- ( N e. Z <-> N e. ( ZZ>= ` M ) ) |
| 3 | 2 | biimpi | |- ( N e. Z -> N e. ( ZZ>= ` M ) ) |
| 4 | eluzelz | |- ( N e. ( ZZ>= ` M ) -> N e. ZZ ) |
|
| 5 | 3 4 | syl | |- ( N e. Z -> N e. ZZ ) |