Metamath Proof Explorer

Theorem n0ssold

Description: The non-negative surreal integers are a subset of the old set of _om . (Contributed by Scott Fenton, 18-Apr-2025)

Ref Expression
Assertion n0ssold 
|- NN0_s C_ ( _Old ` _om )

Proof

Step Hyp Ref Expression
1 omex 
 |-  _om e. _V
2 n0ssoldg 
 |-  ( _om e. _V -> NN0_s C_ ( _Old ` _om ) )
3 1 2 ax-mp 
 |-  NN0_s C_ ( _Old ` _om )