Theorem elfzle3

Description: Membership in a finite set of sequential integer implies the bounds are comparable. (Contributed by NM, 18-Sep-2005) (Revised by Mario Carneiro, 28-Apr-2015)

	Ref	Expression
Assertion	elfzle3	$$⊢K\in \left(M\dots N\right)\to M\le N$$

Proof

Step	Hyp	Ref	Expression
1		elfzuz2	$$⊢K\in \left(M\dots N\right)\to N\in {\mathbb{Z}}_{\ge M}$$
2		eluzle	$$⊢N\in {\mathbb{Z}}_{\ge M}\to M\le N$$
3	1 2	syl	$$⊢K\in \left(M\dots N\right)\to M\le N$$