Metamath Proof Explorer


Theorem slttr

Description: Surreal less than is transitive. (Contributed by Scott Fenton, 16-Jun-2011)

Ref Expression
Assertion slttr
|- ( ( A e. No /\ B e. No /\ C e. No ) -> ( ( A  A 

Proof

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