Prove theorem 1:

Consider the axiomatic system and theorem below:

Axiom 1: For any two points, there exists a line so that each of the two points is on the line.

Axiom 2: There exist at least two points on any line.

Axiom 3: There exist at least three distinct points.

Axiom 4: Not all points are on the same line.

Theorem 1: Each point is on at least two distinct lines.