reserve AS for AffinSpace,
  a,b,c,d,p,q,r,s,x for Element of AS;
reserve AFP for AffinPlane,
  a,a9,b,b9,c,c9,d,p,p9,q,q9,r,x,x9,y,y9,z for Element of AFP,
  A,C,P for Subset of AFP,
  f,g,h,f1,f2 for Permutation of the carrier of AFP;

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;
