Theorem nnne0s

Description: A surreal positive integer is nonzero. (Contributed by Scott Fenton, 15-Apr-2025)

	Ref	Expression
Assertion	nnne0s	$$⊢A\in {\mathbb{N}}_s\to A\ne 0_s$$

Proof

Step	Hyp	Ref	Expression
1		eldifsni	$$⊢A\in \left({\mathbb{N}}_{\mathrm{0s}}\setminus \left\{0_s\right\}\right)\to A\ne 0_s$$
2		df-nns	$$⊢{\mathbb{N}}_s={\mathbb{N}}_{\mathrm{0s}}\setminus \left\{0_s\right\}$$
3	1 2	eleq2s	$$⊢A\in {\mathbb{N}}_s\to A\ne 0_s$$