theorem Th41A:
  PrimeIdeals(A,{1.A}) = {}
  proof
    assume PrimeIdeals(A,{1.A}) <> {}; then
    consider p be object such that
A2: p in PrimeIdeals(A,{1.A}) by XBOOLE_0:def 1;
    consider p1 be prime Ideal of A such that
    p1 = p and
A3: {1.A} c= p1 by A2;
    1.A in {1.A} by TARSKI:def 1;
    hence contradiction by A3,IDEAL_1:19;
  end;
