Metamath Proof Explorer

Theorem n2dvds3

Description: 2 does not divide 3. That means 3 is odd. (Contributed by AV, 28-Feb-2021) (Proof shortened by Steven Nguyen, 3-May-2023)

Ref Expression
Assertion n2dvds3 
|- -. 2 || 3

Proof

Step Hyp Ref Expression
1 3halfnz 
 |-  -. ( 3 / 2 ) e. ZZ
2 3z 
 |-  3 e. ZZ
3 evend2 
 |-  ( 3 e. ZZ -> ( 2 || 3 <-> ( 3 / 2 ) e. ZZ ) )
4 2 3 ax-mp 
 |-  ( 2 || 3 <-> ( 3 / 2 ) e. ZZ )
5 1 4 mtbir 
 |-  -. 2 || 3