Description: The set of all non-negative surreal integers exists. (Contributed by Scott Fenton, 17-Mar-2025)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | n0sex | |- NN0_s e. _V | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | df-n0s | |- NN0_s = ( rec ( ( x e. _V |-> ( x +s 1s ) ) , 0s ) " _om ) | |
| 2 | 1 | a1i | |- ( T. -> NN0_s = ( rec ( ( x e. _V |-> ( x +s 1s ) ) , 0s ) " _om ) ) | 
| 3 | 2 | noseqex | |- ( T. -> NN0_s e. _V ) | 
| 4 | 3 | mptru | |- NN0_s e. _V |