Theorem nnn0sd

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

	Ref	Expression
Hypothesis	nnn0sd.1	$$⊢\phi \to A\in {\mathbb{N}}_s$$
Assertion	nnn0sd	$$⊢\phi \to A\in {\mathbb{N}}_{\mathrm{0s}}$$

Proof

Step	Hyp	Ref	Expression
1		nnn0sd.1	$$⊢\phi \to A\in {\mathbb{N}}_s$$
2		nnssn0s	$$⊢{\mathbb{N}}_s\subseteq {\mathbb{N}}_{\mathrm{0s}}$$
3	2 1	sselid	$$⊢\phi \to A\in {\mathbb{N}}_{\mathrm{0s}}$$