Theorem nnsex

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

	Ref	Expression
Assertion	nnsex	$$⊢{\mathbb{N}}_s\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		df-nns	$$⊢{\mathbb{N}}_s={\mathbb{N}}_{\mathrm{0s}}\setminus \left\{0_s\right\}$$
2		n0sex	$$⊢{\mathbb{N}}_{\mathrm{0s}}\in \mathrm{V}$$
3	2	difexi	$$⊢{\mathbb{N}}_{\mathrm{0s}}\setminus \left\{0_s\right\}\in \mathrm{V}$$
4	1 3	eqeltri	$$⊢{\mathbb{N}}_s\in \mathrm{V}$$