Theorem fznn0sub

Description: Subtraction closure for a member of a finite set of sequential integers. (Contributed by NM, 16-Sep-2005) (Revised by Mario Carneiro, 28-Apr-2015)

	Ref	Expression
Assertion	fznn0sub	|- ( K e. ( M ... N ) -> ( N - K ) e. NN0 )

Proof

Step	Hyp	Ref	Expression
1		elfzuz3	|- ( K e. ( M ... N ) -> N e. ( ZZ>= ` K ) )
2		uznn0sub	|- ( N e. ( ZZ>= ` K ) -> ( N - K ) e. NN0 )
3	1 2	syl	|- ( K e. ( M ... N ) -> ( N - K ) e. NN0 )