Theorem zeo4

Description: An integer is even or odd but not both. With this representation of even and odd integers, this variant of zeo2 follows immediately from the principle of double negation, see notnotb . (Contributed by AV, 17-Jun-2021)

	Ref	Expression
Assertion	zeo4	$$⊢N\in \mathbb{Z}\to \left(2\parallel N\leftrightarrow \neg \neg 2\parallel N\right)$$

Proof

Step	Hyp	Ref	Expression
1		notnotb	$$⊢2\parallel N\leftrightarrow \neg \neg 2\parallel N$$
2	1	a1i	$$⊢N\in \mathbb{Z}\to \left(2\parallel N\leftrightarrow \neg \neg 2\parallel N\right)$$