Description: Membership in a later upper set of integers. (Contributed by Paul Chapman, 22-Nov-2007) Shorten and remove M e. ZZ hypothesis. (Revised by SN, 7-Feb-2025)
Ref | Expression | ||
---|---|---|---|
Hypothesis | eluzaddi.1 | |- K e. ZZ |
|
Assertion | eluzaddi | |- ( N e. ( ZZ>= ` M ) -> ( N + K ) e. ( ZZ>= ` ( M + K ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eluzaddi.1 | |- K e. ZZ |
|
2 | eluzadd | |- ( ( N e. ( ZZ>= ` M ) /\ K e. ZZ ) -> ( N + K ) e. ( ZZ>= ` ( M + K ) ) ) |
|
3 | 1 2 | mpan2 | |- ( N e. ( ZZ>= ` M ) -> ( N + K ) e. ( ZZ>= ` ( M + K ) ) ) |