theorem Th2:
  AFP is Fanoian & a,b // c,d & a,c // b,d & not LIN a,b,c implies
  ex p st LIN b,c,p & LIN a,d,p
proof
  assume ( for a,b,c,d st a,b // c,d & a,c // b,d & a,d // b,c holds LIN a,b,
  c)& a,b // c,d & a,c // b,d & not LIN a,b,c;
  then not a,d // b,c;
  then ex p st LIN a,d,p & LIN b,c,p by AFF_1:60;
  hence thesis;
end;
