Axiom:Propositions of Incidence/Line

Axiom
A (straight) line contains an infinite number of is points, and is completely determined by any two distinct points of that line.

Thus, if a line determined by points $A$ and $B$ also contains the points $X$ and $Y$, then the line determined by points $X$ and $Y$ is the same line, and also contains the points $A$ and $B$.