theorem Th47:
  A <> B implies ex C,D st not {A,B,C,D} is planar
proof
  set P = the PLANE of S;
  assume A <> B;
  then consider C such that
  C on P and
A1: not {A,B,C} is linear by Th44;
  ex D st not {A,B,C,D} is planar by A1,Th45;
  hence thesis;
end;
