theorem Th19:
  not {A,B,C} is linear & {A,B,C} on P & not D on P implies not {A
  ,B,C,D} is planar
proof
  assume that
A1: ( not {A,B,C} is linear)& {A,B,C} on P and
A2: not D on P;
  given Q such that
A3: {A,B,C,D} on Q;
  {A,B,C} \/ {D} on Q by A3,ENUMSET1:6;
  then {A,B,C} on Q by Th9;
  then P = Q by A1,Def13;
  hence contradiction by A2,A3,Th5;
end;
