reserve FCPS for up-3-dimensional CollProjectiveSpace;
reserve a,a9,b,b9,c,c9,d,d9,o,p,q,r,s,t,u,x,y,z for Element of FCPS;

theorem Th16:
  not a,b,c are_collinear & not a9,b9,c9 are_collinear & a,b,c,p
  are_coplanar & a,b,c,q are_coplanar & a,b,c,r are_coplanar & a9,b9,c9,p
are_coplanar & a9,b9,c9,q are_coplanar & a9,b9,c9,r are_coplanar & not a,b,c,a9
  are_coplanar implies p,q,r are_collinear
proof
  assume that
A1: not a,b,c are_collinear and
A2: not a9,b9,c9 are_collinear and
A3: a,b,c,p are_coplanar & a,b,c,q are_coplanar & a,b,c,r are_coplanar and
A4: a9,b9,c9,p are_coplanar & a9,b9,c9,q are_coplanar & a9,b9,c9,r
  are_coplanar and
A5: not a,b,c,a9 are_coplanar;
  a,b,c,a are_coplanar by Th14;
  then
A6: p,q,r,a are_coplanar by A1,A3,Th8;
  a9,b9,c9,a9 are_coplanar by Th14;
  then
A7: p,q,r,a9 are_coplanar by A2,A4,Th8;
  a,b,c,c are_coplanar by Th14;
  then
A8: p,q,r,c are_coplanar by A1,A3,Th8;
  a,b,c,b are_coplanar by Th14;
  then
A9: p,q,r,b are_coplanar by A1,A3,Th8;
  assume not thesis;
  hence contradiction by A5,A6,A9,A8,A7,Th8;
end;
