Three-point geometry axioms:
Axiom 1. There exist exactly three distinct points in the
geometry.
Axiom 2. Each two distinct points are on exactly one line.
Axiom 3. Not all the points of the geometry are on the same line.
Axiom 4. Each two distinct lines are on at least one point.
Prove the following theorems:
Theorem 1: Each two distinct lines are on exactly one point.
Theorem 2. The geometry has exactly three lines.