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
  [x,y,z] in the Collinearity of ProjectiveSpace(V) implies ex p,q,r st
x = Dir(p) & y = Dir(q) & z = Dir(r) & p is not zero & q is not zero & r is not
  zero & p,q,r are_LinDep by Def6;
