Now we turn our attention to general Projective Geometries. Prove that there are at least 4 distinct lines such that no

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Now we turn our attention to general Projective Geometries.
Prove that there are at least 4
distinct lines such that no three are incident at the same
point.
Axioms:
(PA1) A line lies on at least two points.
(PA2) Any two distinct points lie on exactly one line.
(PA3) Any two distinct lines intersect in at least one point.
(PA4) There is a set of four points, no three of which are
collinear.