Theorem gt0ne0s

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

	Ref	Expression
Assertion	gt0ne0s	⊢ ( 0s <s 𝐴 → 𝐴 ≠ 0s )

Proof

Step	Hyp	Ref	Expression
1		0no	⊢ 0s ∈ No
2		ltsne	⊢ ( ( 0s ∈ No ∧ 0s <s 𝐴 ) → 𝐴 ≠ 0s )
3	1 2	mpan	⊢ ( 0s <s 𝐴 → 𝐴 ≠ 0s )