Theorem elfzuz3

Description: Membership in a finite set of sequential integers implies membership in an upper set of integers. (Contributed by NM, 28-Sep-2005) (Revised by Mario Carneiro, 28-Apr-2015)

	Ref	Expression
Assertion	elfzuz3	$$⊢K\in \left(M\dots N\right)\to N\in {\mathbb{Z}}_{\ge K}$$

Proof

Step	Hyp	Ref	Expression
1		elfzuzb	$$⊢K\in \left(M\dots N\right)\leftrightarrow \left(K\in {\mathbb{Z}}_{\ge M}\wedge N\in {\mathbb{Z}}_{\ge K}\right)$$
2	1	simprbi	$$⊢K\in \left(M\dots N\right)\to N\in {\mathbb{Z}}_{\ge K}$$