reserve C for CatStr;
reserve f,g for Morphism of C;
reserve C for non void non empty CatStr,
  f,g for Morphism of C,
  a,b,c,d for Object of C;
reserve o,m for set;
reserve B,C,D for Category;
reserve a,b,c,d for Object of C;
reserve f,f1,f2,g,g1,g2 for Morphism of C;

theorem
  for g being Morphism of C st dom(g) = b holds g(*)(id b) = g
   proof let f be Morphism of C;
    assume
A1:   dom f = b;
     then reconsider ff=f as Morphism of b,cod f by Th3;
      Hom(b,cod f)<>{} by A1,Th1;
     then ff(*)(id b) = ff by Def10;
    hence thesis;
   end;
