Metamath Proof Explorer


Theorem fzo0ssnn0

Description: Half-open integer ranges starting with 0 are subsets of NN0. (Contributed by Thierry Arnoux, 8-Oct-2018) (Proof shortened by JJ, 1-Jun-2021)

Ref Expression
Assertion fzo0ssnn0
|- ( 0 ..^ N ) C_ NN0

Proof

Step Hyp Ref Expression
1 elfzonn0
 |-  ( k e. ( 0 ..^ N ) -> k e. NN0 )
2 1 ssriv
 |-  ( 0 ..^ N ) C_ NN0