Through any two points there exists exactly one line.
A line contains at least two points.
If two lines intersect, then their intersection is exactly one point.
Through any three non-collinear points there exists exactly one plane.
A plane contains at least three non-collinear points.
If two points lie in a plane, then the line containing then lies in the plane.
If two planes intersect, then their intersection is a line.
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