Q:

Group Isomorphism Proof

Is A is isomorphic to B and B is not Isomorphic to C, why does this imply A is not isomorphic to C? 
I understand that if the size of D is not equal to the size of E, this implies D is not isomorphic to E, but unfortunately the implication is the wrong way round for this proof. 

A:

Being isomorphic to is a symmetric transitive relation. 
If $A$ were isomorphic to $C$, then $B$ would be isomorphic to $C$ via $A$, as in $B \cong A \cong C$.