Metamath Proof Explorer


Theorem 0noddALTV

Description: 0 is not an odd number. (Contributed by AV, 3-Feb-2020) (Revised by AV, 17-Jun-2020)

Ref Expression
Assertion 0noddALTV
|- 0 e/ Odd

Proof

Step Hyp Ref Expression
1 0evenALTV
 |-  0 e. Even
2 df-nel
 |-  ( 0 e/ Odd <-> -. 0 e. Odd )
3 0z
 |-  0 e. ZZ
4 zeo2ALTV
 |-  ( 0 e. ZZ -> ( 0 e. Even <-> -. 0 e. Odd ) )
5 4 bicomd
 |-  ( 0 e. ZZ -> ( -. 0 e. Odd <-> 0 e. Even ) )
6 3 5 ax-mp
 |-  ( -. 0 e. Odd <-> 0 e. Even )
7 2 6 bitri
 |-  ( 0 e/ Odd <-> 0 e. Even )
8 1 7 mpbir
 |-  0 e/ Odd