Theorem fzct

Description: A finite set of sequential integer is countable. (Contributed by Glauco Siliprandi, 8-Apr-2021)

	Ref	Expression
Assertion	fzct	$$⊢\left(N\dots M\right)\preccurlyeq \mathrm{\omega }$$

Proof

Step	Hyp	Ref	Expression
1		fzssz	$$⊢\left(N\dots M\right)\subseteq \mathbb{Z}$$
2		zct	$$⊢\mathbb{Z}\preccurlyeq \mathrm{\omega }$$
3		ssct	$$⊢\left(\left(N\dots M\right)\subseteq \mathbb{Z}\wedge \mathbb{Z}\preccurlyeq \mathrm{\omega }\right)\to \left(N\dots M\right)\preccurlyeq \mathrm{\omega }$$
4	1 2 3	mp2an	$$⊢\left(N\dots M\right)\preccurlyeq \mathrm{\omega }$$