reserve V for RealLinearSpace;
reserve p,q,r,u,v,w,y,u1,v1,w1 for Element of V;
reserve a,b,c,d,a1,b1,c1,a2,b2,c2,a3,b3,e,f for Real;
reserve x,y,z for object;
reserve V for non trivial RealLinearSpace;
reserve p,q,r,u,v,w for Element of V;

theorem Th21:
  p is not zero implies Dir(p) is Element of ProjectivePoints(V)
proof
  assume p is not zero;
  then p in NonZero V by STRUCT_0:1;
  then Dir(p) in Class Proportionality_as_EqRel_of V by EQREL_1:def 3;
  hence thesis by Def5;
end;
