Please , Not delete my answer, because is correct.
It is false that any three points are containded in exactly one plane.
For example: if the points are aligned, these points aren´t containded in a plane, these points are containded in a line.
O= point.
--------------O-----------O---------O--------- (these points are contaided in a line).
o o (these points are contained in a plane)
o