reserve U0 for Universal_Algebra,
  U1 for SubAlgebra of U0,
  o for operation of U0;

theorem Th1:
  for u being object holds u in Sub(U0) iff ex U1 be strict SubAlgebra
  of U0 st u = U1
proof
  let u be object;
  thus u in Sub(U0) implies ex U1 being strict SubAlgebra of U0 st u = U1
  proof
    assume u in Sub(U0);
    then u is strict SubAlgebra of U0 by UNIALG_2:def 14;
    hence thesis;
  end;
  thus thesis by UNIALG_2:def 14;
end;
