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Metamath Proof Explorer

Theorem nnnfi

Description: The set of positive integers is infinite. (Contributed by Glauco Siliprandi, 11-Oct-2020)

		Ref	Expression
	Assertion	nnnfi	$⊢ \neg ℕ \in Fin$

Step	Hyp	Ref	Expression
1		1z	$⊢ 1 \in ℤ$
2		nnuz	$⊢ ℕ = ℤ_{\geq 1}$
3	2	uzinf	$⊢ 1 \in ℤ \to \neg ℕ \in Fin$
4	1 3	ax-mp	$⊢ \neg ℕ \in Fin$