theorem Th35:
  A <> B & C on Line(A,B) implies {A,B,C} is linear
proof
  assume A <> B;
  then {A,B} on Line(A,B) by Def19;
  then
A1: A on Line(A,B) & B on Line(A,B) by Th1;
  assume C on Line(A,B);
  then {A,B,C} on Line(A,B) by A1,Th2;
  hence thesis;
end;
