reserve SAS for AffinPlane;

theorem
  ex SAS st (for o,a,a9,b,b9,c,c9 being Element of SAS holds ( not o,a
// o,b & not o,a // o,c & o,a // o,a9 & o,b // o,b9 & o,c // o,c9 & a,b // a9,
  b9 & a,c // a9,c9 implies b,c // b9,c9 )) & (for a,a9,b,b9,c,c9 being Element
of SAS holds ( not a,a9 // a,b & not a,a9 // a,c & a,a9 // b,b9 & a,a9 // c,c9
& a,b // a9,b9 & a,c // a9,c9 implies b,c // b9,c9 )) & (for a1,a2,a3,b1,b2,b3
being Element of SAS holds ( a1,a2 // a1,a3 & b1,b2 // b1,b3 & a1,b2 // a2,b1 &
  a2,b3 // a3,b2 implies a3,b1 // a1,b3 )) & for a,b,c,d being Element of SAS
  holds ( not a,b // a,c & a,b // c,d & a,c // b,d implies not a,d // b,c )
proof
  set PAS = the Fanoian Pappian Desarguesian translational AffinPlane;
  reconsider SAS=PAS as AffinPlane;
  take SAS;
  thus thesis by Th1,Th2,Th3,PAPDESAF:def 1;
end;
