Metamath Proof Explorer


Theorem fzonnsub2

Description: If M < N then N - M is a positive integer. (Contributed by Mario Carneiro, 1-Jan-2017)

Ref Expression
Assertion fzonnsub2
|- ( K e. ( M ..^ N ) -> ( N - M ) e. NN )

Proof

Step Hyp Ref Expression
1 elfzolt3b
 |-  ( K e. ( M ..^ N ) -> M e. ( M ..^ N ) )
2 fzonnsub
 |-  ( M e. ( M ..^ N ) -> ( N - M ) e. NN )
3 1 2 syl
 |-  ( K e. ( M ..^ N ) -> ( N - M ) e. NN )