Playfair's axiom states:
Through any point in the plane, there is at most one straight line parallel to a given straight line.
This axiom is equivalent to the parallel postulate.
If the point $P$ lies on the given straight line $\mathcal{l}$, our intuition tells us that there are no straight lines through $P$ that are parallel to $\mathcal{l}$. This is because any straight line passing through $P$ either intersects $\mathcal{l}$ at one point, namely $P$, (which means they are not parallel) or is $\mathcal{l}$ itself (a line cannot be parallel to itself).
This seems obvious to me but have I implicitly used Playfair's axiom or any of the first four postulates?