Proposition 5.3: The three secondary baselines at the points of intersection of three non-concurrent primary baselines are concurrent.
Pf: Any three planes of PG(3,q) which do not contain a common line meet at a unique point, since two of the planes intersect in a line and this line must meet the third plane in a point. The three planes which determine the three non-concurrent primary baselines can not contain a common line, otherwise the primary baselines would be concurrent. Thus, they meet at a unique point not in . The projection of this point into lies on the projections of the three lines of intersection of these three planes, that is, there is a point in common with the three secondary baselines which are these projections.