Theorem elfz3nn0

Description: The upper bound of a nonempty finite set of sequential nonnegative integers is a nonnegative integer. (Contributed by NM, 16-Sep-2005) (Revised by Mario Carneiro, 28-Apr-2015)

	Ref	Expression
Assertion	elfz3nn0	$$⊢K\in \left(0\dots N\right)\to N\in {\mathbb{N}}_0$$

Proof

Step	Hyp	Ref	Expression
1		elfz2nn0	$$⊢K\in \left(0\dots N\right)\leftrightarrow \left(K\in {\mathbb{N}}_0\wedge N\in {\mathbb{N}}_0\wedge K\le N\right)$$
2	1	simp2bi	$$⊢K\in \left(0\dots N\right)\to N\in {\mathbb{N}}_0$$