reserve x,y,z for Real,
  x3,y3 for Real,
  p for Point of TOP-REAL 3;
reserve p1,p2,p3,p4 for Point of TOP-REAL 3,
  x1,x2,y1,y2,z1,z2 for Real;

theorem Th17:
  p1<X>p2 = - p2<X>p1
proof
  - p2 <X> p1 = (-1)*(p2 <X> p1) by RLVECT_1:16
    .= |[ (-1) * ( (p2`2 * p1`3) - (p2`3 * p1`2) ), (-1) * ( (p2`3 * p1`1) -
  (p2`1 * p1`3) ), (-1) * ( (p2`1 * p1`2) - (p2`2 * p1`1) ) ]| by Th8
    .= p1 <X> p2;
  hence thesis;
end;
