Theorem elfzuz

Description: A member of a finite set of sequential integers belongs to an upper set of integers. (Contributed by NM, 17-Sep-2005) (Revised by Mario Carneiro, 28-Apr-2015)

	Ref	Expression
Assertion	elfzuz	|- ( K e. ( M ... N ) -> K e. ( ZZ>= ` M ) )

Proof

Step	Hyp	Ref	Expression
1		elfzuzb	|- ( K e. ( M ... N ) <-> ( K e. ( ZZ>= ` M ) /\ N e. ( ZZ>= ` K ) ) )
2	1	simplbi	|- ( K e. ( M ... N ) -> K e. ( ZZ>= ` M ) )