Theorem eluz5nn

Description: An integer greater than or equal to 5 is a positive integer. (Contributed by AV, 22-Nov-2025)

	Ref	Expression
Assertion	eluz5nn	$$⊢N\in {\mathbb{Z}}_{\ge 5}\to N\in \mathbb{N}$$

Proof

Step	Hyp	Ref	Expression
1		uzuzle35	$$⊢N\in {\mathbb{Z}}_{\ge 5}\to N\in {\mathbb{Z}}_{\ge 3}$$
2		eluz3nn	$$⊢N\in {\mathbb{Z}}_{\ge 3}\to N\in \mathbb{N}$$
3	1 2	syl	$$⊢N\in {\mathbb{Z}}_{\ge 5}\to N\in \mathbb{N}$$