Metamath Proof Explorer


Theorem oddm1d2

Description: An integer is odd iff its predecessor divided by 2 is an integer. This is another representation of odd numbers without using the divides relation. (Contributed by AV, 18-Jun-2021) (Proof shortened by AV, 22-Jun-2021)

Ref Expression
Assertion oddm1d2 N¬2NN12

Proof

Step Hyp Ref Expression
1 oddp1d2 N¬2NN+12
2 zob NN+12N12
3 1 2 bitrd N¬2NN12