theorem Th18:
  p<>q & p in P & q in P implies Line(p,q) c= P
proof
  assume that
A1: p<>q and
A2: p in P & q in P;
  let x be object;
  consider a,b such that
  a<>b and
A3: P = Line(a,b) by Def7;
  assume x in Line(p,q);
  then consider r be Point of CLSP such that
A4: r=x and
A5: p,q,r are_collinear;
  a,b,p are_collinear & a,b,q are_collinear by A2,A3,Th11;
  then a,b,r are_collinear by A1,A5,Th9;
  hence thesis by A3,A4;
end;
