Theorem elfzonn0

Description: A member of a half-open range of nonnegative integers is a nonnegative integer. (Contributed by Alexander van der Vekens, 21-May-2018)

	Ref	Expression
Assertion	elfzonn0	$$⊢K\in \left(0..^N\right)\to K\in {\mathbb{N}}_0$$

Proof

Step	Hyp	Ref	Expression
1		elfzouz	$$⊢K\in \left(0..^N\right)\to K\in {\mathbb{Z}}_{\ge 0}$$
2		elnn0uz	$$⊢K\in {\mathbb{N}}_0\leftrightarrow K\in {\mathbb{Z}}_{\ge 0}$$
3	1 2	sylibr	$$⊢K\in \left(0..^N\right)\to K\in {\mathbb{N}}_0$$