reserve CPS for proper CollSp,
  B for Subset of CPS,
  p for Point of CPS,
  x, y, z, Y for set;
reserve a,b,c,p,q for POINT of IncProjSp_of(CPS),
  P,Q for LINE of IncProjSp_of(CPS),
  a9,b9,c9,p9,q9,r9 for Point of CPS,
  P9 for LINE of CPS;

theorem Th6:
  ex a9, b9, c9 st a9<>b9 & b9<>c9 & c9<>a9
proof
  consider a99, b99, c99 being Point of CPS such that
A1: not a99,b99,c99 are_collinear by COLLSP:def 6;
A2: c99<>a99 by A1,COLLSP:2;
  a99<>b99 & b99<>c99 by A1,COLLSP:2;
  hence thesis by A2;
end;
