reserve o,m for set;

theorem Th9:
  for c being Object of c1Cat(o,m), p1,p2 being Morphism of c1Cat(
  o,m) holds c is_a_product_wrt p1,p2
proof
  let c be Object of c1Cat(o,m), p1,p2 be Morphism of c1Cat(o,m);
  thus dom p1 = c & dom p2 = c by Th3;
  let d be Object of c1Cat(o,m),f,g be Morphism of c1Cat(o,m) such that
  f in Hom(d,cod p1) and
  g in Hom(d,cod p2);
  take h = p1;
  thus h in Hom(d,c) by Th5;
  thus thesis by Th4;
end;
