Metamath Proof Explorer

Theorem gt0ne0sd

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

Ref Expression
Hypothesis gt0ne0sd.1 
|- ( ph -> 0s
Assertion gt0ne0sd 
|- ( ph -> A =/= 0s )

Proof

Step Hyp Ref Expression
1 gt0ne0sd.1 
 |-  ( ph -> 0s
2 gt0ne0s 
 |-  ( 0s  A =/= 0s )
3 1 2 syl 
 |-  ( ph -> A =/= 0s )