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;
