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.
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