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
  for f being Morphism of a,b for h being Morphism of c,d st Hom(a,b) <>
  {} & Hom(c,d) <> {} & f = h holds a = c & b = d
proof
  let f be Morphism of a,b;
  let h be Morphism of c,d;
  assume that
A1: Hom(a,b) <> {} and
A2: Hom(c,d) <> {};
  dom(f) = a & cod(f) = b by A1,Th4;
  hence thesis by A2,Th4;
end;
