Given qa, qb, qc as points at infinity, co-planar lying on the plane P:

if a plane contains non-ideal points it intersects the ideal plane in a line:
  the plane cannot be the ideal plane
  all distinct planes intersect in a line
  -> a plane containing non-ideal points will intersect the ideal plane in a line at infinity

qa,qb,qc lie on the ideal plane
qa,qb,qc lie on P
-> qa,qb,qc lie on the intersection of P and the ideal plane
P and the ideal plane intersect in a line at infinity
-> qa,qb,qc are co-linear