Description: Alternate characterizations of an odd number. (Contributed by AV, 7-Jun-2020)
Ref | Expression | ||
---|---|---|---|
Assertion | zob | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | peano2zm | |
|
2 | peano2z | |
|
3 | peano2z | |
|
4 | 3 | zcnd | |
5 | 4 | halfcld | |
6 | npcan1 | |
|
7 | 5 6 | syl | |
8 | 7 | eqcomd | |
9 | 8 | eleq1d | |
10 | 2 9 | syl5ibr | |
11 | 1 10 | impbid2 | |
12 | zcn | |
|
13 | xp1d2m1eqxm1d2 | |
|
14 | 12 13 | syl | |
15 | 14 | eleq1d | |
16 | 11 15 | bitrd | |