Theorem elfzle2

Description: A member of a finite set of sequential integer is less than or equal to the upper bound. (Contributed by NM, 6-Sep-2005) (Revised by Mario Carneiro, 28-Apr-2015)

	Ref	Expression
Assertion	elfzle2	$$⊢K\in \left(M\dots N\right)\to K\le N$$

Proof

Step	Hyp	Ref	Expression
1		elfzuz3	$$⊢K\in \left(M\dots N\right)\to N\in {\mathbb{Z}}_{\ge K}$$
2		eluzle	$$⊢N\in {\mathbb{Z}}_{\ge K}\to K\le N$$
3	1 2	syl	$$⊢K\in \left(M\dots N\right)\to K\le N$$