Metamath Proof Explorer


Theorem sgt0ne0d

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

Ref Expression
Hypothesis sgt0ne0d.1 φ 0 s < s A
Assertion sgt0ne0d φ A 0 s

Proof

Step Hyp Ref Expression
1 sgt0ne0d.1 φ 0 s < s A
2 sgt0ne0 0 s < s A A 0 s
3 1 2 syl φ A 0 s