Theorem eluz3nn

Description: An integer greater than or equal to 3 is a positive integer. (Contributed by Alexander van der Vekens, 17-Sep-2018) (Proof shortened by AV, 30-Nov-2025)

	Ref	Expression
Assertion	eluz3nn	$$⊢N\in {\mathbb{Z}}_{\ge 3}\to N\in \mathbb{N}$$

Proof

Step	Hyp	Ref	Expression
1		uzuzle23	$$⊢N\in {\mathbb{Z}}_{\ge 3}\to N\in {\mathbb{Z}}_{\ge 2}$$
2		eluz2nn	$$⊢N\in {\mathbb{Z}}_{\ge 2}\to N\in \mathbb{N}$$
3	1 2	syl	$$⊢N\in {\mathbb{Z}}_{\ge 3}\to N\in \mathbb{N}$$