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 e. ZZ -> ( 2 || N <-> -. -. 2 || N ) )

Proof

Step	Hyp	Ref	Expression
1		notnotb	|- ( 2 || N <-> -. -. 2 || N )
2	1	a1i	|- ( N e. ZZ -> ( 2 || N <-> -. -. 2 || N ) )