Metamath Proof Explorer


Theorem ssbri

Description: Inference from a subclass relationship of binary relations. (Contributed by NM, 28-Mar-2007) (Revised by Mario Carneiro, 8-Feb-2015)

Ref Expression
Hypothesis ssbri.1
|- A C_ B
Assertion ssbri
|- ( C A D -> C B D )

Proof

Step Hyp Ref Expression
1 ssbri.1
 |-  A C_ B
2 ssbr
 |-  ( A C_ B -> ( C A D -> C B D ) )
3 1 2 ax-mp
 |-  ( C A D -> C B D )