Theorem elfznn0

Description: A member of a finite set of sequential nonnegative integers is a nonnegative integer. (Contributed by NM, 5-Aug-2005) (Revised by Mario Carneiro, 28-Apr-2015)

	Ref	Expression
Assertion	elfznn0	|- ( K e. ( 0 ... N ) -> K e. NN0 )

Proof

Step	Hyp	Ref	Expression
1		elfz2nn0	|- ( K e. ( 0 ... N ) <-> ( K e. NN0 /\ N e. NN0 /\ K <_ N ) )
2	1	simp1bi	|- ( K e. ( 0 ... N ) -> K e. NN0 )