Theorem sgt0ne0

Description: A positive surreal is not equal to zero. (Contributed by Scott Fenton, 12-Mar-2025)

	Ref	Expression
Assertion	sgt0ne0	$$⊢0_s{<}_{s}A\to A\ne 0_s$$

Proof

Step	Hyp	Ref	Expression
1		0sno	$$⊢0_s\in \mathrm{No}$$
2		sltne	$$⊢\left(0_s\in \mathrm{No}\wedge 0_s{<}_{s}A\right)\to A\ne 0_s$$
3	1 2	mpan	$$⊢0_s{<}_{s}A\to A\ne 0_s$$