PL-OM 2010 Problem 4

On the side $BC$ of the triangle $ABC$ there are two points $D$ and $E$ such that $BD < BE$ . Denote by $p_1$ and $p_2$ the perimeters of triangles $ABC$ and $ADE$ respectively. Prove that $$p_1 > p_2 + 2\cdot \min\{BD, EC\}.$$