Metamath Proof Explorer


Theorem elfzelz

Description: A member of a finite set of sequential integer 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 )