Metamath Proof Explorer

Theorem sstr

Description: Transitivity of subclass relationship. Theorem 6 of Suppes p. 23. (Contributed by NM, 5-Sep-2003)

Ref Expression
Assertion sstr 
|- ( ( A C_ B /\ B C_ C ) -> A C_ C )

Proof

Step Hyp Ref Expression
1 sstr2 
 |-  ( A C_ B -> ( B C_ C -> A C_ C ) )
2 1 imp 
 |-  ( ( A C_ B /\ B C_ C ) -> A C_ C )