theorem Th44:
  A <> B implies ex C st C on P & not {A,B,C} is linear
proof
  consider L such that
A1: {A,B} on L by Def9;
  consider C,D,E such that
A2: {C,D,E} on P and
A3: not {C,D,E} is linear by Th41;
A4: C on P & D on P by A2,Th4;
  not {C,D,E} on L by A3;
  then
A5: not C on L or not D on L or not E on L by Th2;
A6: E on P by A2,Th4;
  assume A <> B;
  then
  not {A,B,C} is linear or not {A,B,D} is linear or not {A,B,E} is linear
  by A1,A5,Th18;
  hence thesis by A4,A6;
end;
