reserve o,m for set;
reserve C for Cartesian_category;
reserve a,b,c,d,e,s for Object of C;

theorem Th31:
  Hom(a[x]b,b[x]a)<>{}
proof
  Hom(a[x]b,a) <> {} & Hom(a[x]b,b) <> {} by Th19;
  hence thesis by Th23;
end;
