Theorem eluzelz2d

Description: A member of an upper set of integers is an integer. (Contributed by Glauco Siliprandi, 23-Oct-2021)

	Ref	Expression
Hypotheses	eluzelz2d.1	$$⊢Z={\mathbb{Z}}_{\ge M}$$
	eluzelz2d.2	$$⊢\phi \to N\in Z$$
Assertion	eluzelz2d	$$⊢\phi \to N\in \mathbb{Z}$$

Proof

Step	Hyp	Ref	Expression
1		eluzelz2d.1	$$⊢Z={\mathbb{Z}}_{\ge M}$$
2		eluzelz2d.2	$$⊢\phi \to N\in Z$$
3	1	eluzelz2	$$⊢N\in Z\to N\in \mathbb{Z}$$
4	2 3	syl	$$⊢\phi \to N\in \mathbb{Z}$$