A Finite Projective Geometry Exercise 1.20.
The essence of mathematics is not to make simple things complicated, but to make complicated things simple.
—Stanley Gudder

Exercise 1.20.  Prove Theorem P4. In a projective plane of order n, every line is incident with exactly n + 1 points.

Since the finite projective plane satisfies the principle of duality, Theorem P4 follows immediately from Theorem P3.