Theorem gt0ne0sd

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

	Ref	Expression
Hypothesis	gt0ne0sd.1	⊢ ( 𝜑 → 0s <s 𝐴 )
Assertion	gt0ne0sd	⊢ ( 𝜑 → 𝐴 ≠ 0s )

Proof

Step	Hyp	Ref	Expression
1		gt0ne0sd.1	⊢ ( 𝜑 → 0s <s 𝐴 )
2		gt0ne0s	⊢ ( 0s <s 𝐴 → 𝐴 ≠ 0s )
3	1 2	syl	⊢ ( 𝜑 → 𝐴 ≠ 0s )