reserve IPS for IncProjSp,
  z for POINT of IPS;
reserve IPP for Desarguesian 2-dimensional IncProjSp,
  a,b,c,d,p,pp9,q,o,o9,o99 ,oo9 for POINT of IPP,
  r,s,x,y,o1,o2 for POINT of IPP,
  O1,O2,O3,O4,A,B,C,O,Q,Q1 ,Q2,Q3,R,S,X for LINE of IPP;

theorem
  not o1 on O1 & not o1 on O2 & not o2 on O2 & not o2 on O3 & O1,O2,O3
are_concurrent & O1<>O3 implies ex o st not o on O1 & not o on O3 & IncProj(O2,
  o2,O3)*IncProj(O1,o1,O2) = IncProj(O1,o,O3)
by PROJRED1:25;
