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;

theorem
  Hom(dom(f),cod(f)) <> {} by Th1;

definition
  let C,a,b;
  assume
A1: Hom(a,b)<>{};
  mode Morphism of a,b -> Morphism of C means
:Def3: it in Hom(a,b);
  existence by A1,SUBSET_1:4;
