theorem Th24:
  |{p2,p6,p7}| = 0 implies
  |{p2,p4,p7}| * |{p2,p6,p8}| = - |{p2,p4,p6}| * |{p2,p8,p7}|
  proof
    assume
A1: |{p2,p6,p7}| = 0;
A2: |{p2,p7,p6}| = - |{p2,p6,p7}| & |{p2,p7,p8}| = - |{p2,p8,p7}|
      by ANPROJ_8:29;
    |{p2,p4,p7}| * |{p2,p6,p8}| - |{p2,p4,p6}| * |{p2,p7,p8}| + |{p2,p4,p8}|
      * |{p2,p7,p6}| = 0 by ANPROJ_8:28;
    hence thesis by A1,A2;
  end;
