Theorem uzid2

Description: Membership of the least member in an upper set of integers. (Contributed by Glauco Siliprandi, 23-Oct-2021)

	Ref	Expression
Assertion	uzid2	$$⊢M\in {\mathbb{Z}}_{\ge N}\to M\in {\mathbb{Z}}_{\ge M}$$

Proof

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