Theorem elfzelzd

Description: A member of a finite set of sequential integers is an integer. (Contributed by Glauco Siliprandi, 5-Apr-2020)

	Ref	Expression
Hypothesis	elfzelzd.1	$$⊢\phi \to K\in \left(M\dots N\right)$$
Assertion	elfzelzd	$$⊢\phi \to K\in \mathbb{Z}$$

Proof

Step	Hyp	Ref	Expression
1		elfzelzd.1	$$⊢\phi \to K\in \left(M\dots N\right)$$
2		elfzelz	$$⊢K\in \left(M\dots N\right)\to K\in \mathbb{Z}$$
3	1 2	syl	$$⊢\phi \to K\in \mathbb{Z}$$