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 ) |