theorem Th4:
  for a,b being Object of 1Cat(x,y) holds Hom(a,b) = {y}
proof
  let a,b be Object of 1Cat(x,y);
  thus Hom(a,b) c= {y};
  y is Morphism of 1Cat(x,y) by TARSKI:def 1;
  then y in Hom(a,b) by CAT_1:11;
  hence thesis by ZFMISC_1:31;
end;
