Description: An integer is even iff its quotient with 2 is an integer. This is a representation of even numbers without using the divides relation, see zeo and zeo2 . (Contributed by AV, 22-Jun-2021)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | evend2 | |- ( N e. ZZ -> ( 2 || N <-> ( N / 2 ) e. ZZ ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 2z | |- 2 e. ZZ |
|
| 2 | 2ne0 | |- 2 =/= 0 |
|
| 3 | dvdsval2 | |- ( ( 2 e. ZZ /\ 2 =/= 0 /\ N e. ZZ ) -> ( 2 || N <-> ( N / 2 ) e. ZZ ) ) |
|
| 4 | 1 2 3 | mp3an12 | |- ( N e. ZZ -> ( 2 || N <-> ( N / 2 ) e. ZZ ) ) |