theorem Th23:
  |{p2,p4,p9}| = 0 implies
  |{p2,p4,p5}| * |{p2,p9,p7}| = - |{p2,p4,p7}| * |{p2,p5,p9}|
  proof
    assume
A1: |{p2,p4,p9}| = 0;
    |{p2,p4,p5}| * |{p2,p9,p7}| - |{p2,p4,p9}| * |{p2,p5,p7}| +
      |{p2,p4,p7}| * |{p2,p5,p9}| = 0 by ANPROJ_8:28;
    hence thesis by A1;
  end;
