theorem Th23:
  Hom(c,a) <> {} & Hom(c,b) <> {} implies Hom(c,a[x]b) <> {}
proof
A1: a[x]b is_a_product_wrt pr1(a,b),pr2(a,b) by Def8;
  Hom(a[x]b,a) <> {} & Hom(a[x]b,b) <> {} by Th19;
  hence thesis by A1,CAT_3:55;
end;
