reserve SAS for Semi_Affine_Space;
reserve a,a9,a1,a2,a3,a4,b,b9,c,c9,d,d9,d1,d2,o,p,p1,p2,q,r,r1,r2,s,x, y,t,z
  for Element of SAS;

theorem Th6:
  a,b // c,d implies b,a // c,d & a,b // d,c & b,a // d,c & c,d //
  a,b & d,c // a,b & c,d // b,a & d,c // b,a
proof
  assume a,b // c,d;
  then c,d // a,b by Th2;
  then
A1: d,c // a,b by Th4;
  then
A2: d,c // b,a by Th5;
  then c,d // b,a by Th4;
  hence thesis by A1,A2,Th2,Th4;
end;
