Theorem eluzelzd

Description: A member of an upper set of integers is an integer. (Contributed by Glauco Siliprandi, 8-Apr-2021)

	Ref	Expression
Hypothesis	eluzelzd.1	$$⊢\phi \to N\in {\mathbb{Z}}_{\ge M}$$
Assertion	eluzelzd	$$⊢\phi \to N\in \mathbb{Z}$$

Proof

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