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 
|- ( ph -> 0s
Assertion sgt0ne0d 
|- ( ph -> A =/= 0s )

Proof

Step Hyp Ref Expression
1 sgt0ne0d.1 
 |-  ( ph -> 0s
2 sgt0ne0 
 |-  ( 0s  A =/= 0s )
3 1 2 syl 
 |-  ( ph -> A =/= 0s )