Description: No even integer equals an odd integer (i.e. no integer can be both even and odd). Exercise 10(a) of Apostol p. 28. (Contributed by NM, 31-Jul-2004) (Revised by AV, 16-Jun-2020)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | zneoALTV | |- ( ( A e. Even /\ B e. Odd ) -> A =/= B ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | oddneven | |- ( B e. Odd -> -. B e. Even ) |
|
| 2 | nelne2 | |- ( ( A e. Even /\ -. B e. Even ) -> A =/= B ) |
|
| 3 | 1 2 | sylan2 | |- ( ( A e. Even /\ B e. Odd ) -> A =/= B ) |