Theorem n0sex

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

Proof

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