Theorem nnn0s

Description: A positive surreal integer is a non-negative surreal integer. (Contributed by Scott Fenton, 26-May-2025)

	Ref	Expression
Assertion	nnn0s	$$⊢A\in {\mathbb{N}}_s\to A\in {\mathbb{N}}_{\mathrm{0s}}$$

Proof

Step	Hyp	Ref	Expression
1		nnssn0s	$$⊢{\mathbb{N}}_s\subseteq {\mathbb{N}}_{\mathrm{0s}}$$
2	1	sseli	$$⊢A\in {\mathbb{N}}_s\to A\in {\mathbb{N}}_{\mathrm{0s}}$$