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Metamath Proof Explorer

Theorem fzoct

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

		Ref	Expression
	Assertion	fzoct	$⊢ (N ..^M) ≼ ω$

Step	Hyp	Ref	Expression
1		fzossz	$⊢ (N ..^M) \subseteq ℤ$
2		zct	$⊢ ℤ ≼ ω$
3		ssct	$⊢ ((N ..^M) \subseteq ℤ \land ℤ ≼ ω) \to (N ..^M) ≼ ω$
4	1 2 3	mp2an	$⊢ (N ..^M) ≼ ω$