Theorem n0sex

Description: The set of all non-negative surreal integers exists. (Contributed by Scott Fenton, 17-Mar-2025)

	Ref	Expression
Assertion	n0sex	$$⊢{\mathbb{N}}_{\mathrm{0s}}\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		omex	$$⊢\mathrm{\omega }\in \mathrm{V}$$
2		n0sexg	$$⊢\mathrm{\omega }\in \mathrm{V}\to {\mathbb{N}}_{\mathrm{0s}}\in \mathrm{V}$$
3	1 2	ax-mp	$$⊢{\mathbb{N}}_{\mathrm{0s}}\in \mathrm{V}$$