Theorem nnzsd

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

	Ref	Expression
Hypothesis	nnzsd.1	$$⊢\phi \to A\in {\mathbb{N}}_s$$
Assertion	nnzsd	$$⊢\phi \to A\in {\mathbb{Z}}_s$$

Proof

Step	Hyp	Ref	Expression
1		nnzsd.1	$$⊢\phi \to A\in {\mathbb{N}}_s$$
2		nnzs	$$⊢A\in {\mathbb{N}}_s\to A\in {\mathbb{Z}}_s$$
3	1 2	syl	$$⊢\phi \to A\in {\mathbb{Z}}_s$$