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 Th1:
  A=B or B=C or C=A implies A,B,C are_concurrent
proof
A1: ( ex a st a on B & a on C)& ex b st b on C & b on A by INCPROJ:def 9;
  assume A=B or B=C or C=A;
  hence thesis by A1;
end;
