Metamath Proof Explorer

Theorem gt0ne0s

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

Ref Expression
Assertion gt0ne0s 
|- ( 0s  A =/= 0s )

Proof

Step Hyp Ref Expression
1 0no 
 |-  0s e. No
2 ltsne 
 |-  ( ( 0s e. No /\ 0s  A =/= 0s )
3 1 2 mpan 
 |-  ( 0s  A =/= 0s )