SILK-ROAD 2006 Problem 4

A family $L$ of 2006 lines on the plane is given in such a way that it doesn't contain parallel lines and it doesn't contain three lines with a common point.We say that the line $l_1\in L$ is bounding the line $l_2\in L$ ,if all intersection points of the line $l_2$ with other lines from $L$ lie on the one side of the line $l_1$ . Prove that in the family $L$ there are two lines $l$ and $l'$ such that the following 2 conditions are satisfied simultaneously: 1) The line $l$ is bounding the line $l'$ ; 2) the line $l'$ is not bounding the line $l$ .