Theorem 2ndvdsodd

Description: 2 does not divide an odd number. (Contributed by AV, 18-Jun-2020)

	Ref	Expression
Assertion	2ndvdsodd	$$⊢Z\in \mathrm{Odd}\to \neg 2\parallel Z$$

Proof

Step	Hyp	Ref	Expression
1		isodd3	$$⊢Z\in \mathrm{Odd}\leftrightarrow \left(Z\in \mathbb{Z}\wedge \neg 2\parallel Z\right)$$
2	1	simprbi	$$⊢Z\in \mathrm{Odd}\to \neg 2\parallel Z$$