Theorem n0zsd

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

	Ref	Expression
Hypothesis	n0zsd.1	$$⊢\phi \to A\in {\mathbb{N}}_{\mathrm{0s}}$$
Assertion	n0zsd	$$⊢\phi \to A\in {\mathbb{Z}}_s$$

Proof

Step	Hyp	Ref	Expression
1		n0zsd.1	$$⊢\phi \to A\in {\mathbb{N}}_{\mathrm{0s}}$$
2		n0zs	$$⊢A\in {\mathbb{N}}_{\mathrm{0s}}\to A\in {\mathbb{Z}}_s$$
3	1 2	syl	$$⊢\phi \to A\in {\mathbb{Z}}_s$$