Theorem elfz3nn0

Description: The upper bound of a nonempty finite set of sequential nonnegative integers is a nonnegative integer. (Contributed by NM, 16-Sep-2005) (Revised by Mario Carneiro, 28-Apr-2015)

	Ref	Expression
Assertion	elfz3nn0	|- ( K e. ( 0 ... N ) -> N e. NN0 )

Proof

Step	Hyp	Ref	Expression
1		elfz2nn0	|- ( K e. ( 0 ... N ) <-> ( K e. NN0 /\ N e. NN0 /\ K <_ N ) )
2	1	simp2bi	|- ( K e. ( 0 ... N ) -> N e. NN0 )