Metamath Proof Explorer


Theorem slttrine

Description: Trichotomy law for surreals. (Contributed by Scott Fenton, 23-Nov-2021)

Ref Expression
Assertion slttrine
|- ( ( A e. No /\ B e. No ) -> ( A =/= B <-> ( A 

Proof

Step Hyp Ref Expression
1 sltso
 |-  
2 sotrine
 |-  ( (  ( A =/= B <-> ( A 
3 1 2 mpan
 |-  ( ( A e. No /\ B e. No ) -> ( A =/= B <-> ( A