Theorem elfzelz

Description: A member of a finite set of sequential integers is an integer. (Contributed by NM, 6-Sep-2005) (Revised by Mario Carneiro, 28-Apr-2015)

	Ref	Expression
Assertion	elfzelz	|- ( K e. ( M ... N ) -> K e. ZZ )

Proof

Step	Hyp	Ref	Expression
1		elfzuz	|- ( K e. ( M ... N ) -> K e. ( ZZ>= ` M ) )
2		eluzelz	|- ( K e. ( ZZ>= ` M ) -> K e. ZZ )
3	1 2	syl	|- ( K e. ( M ... N ) -> K e. ZZ )