MathNet 2011 Question 74

Let $\triangle ABC$ be a triangle with $AB \leq AC$ and let $P$ be an interior point on the angle bisector of $\angle BAC$. Let $D, E$ be points on the segments $PC, PB$ respectively such that $\angle PBD = \angle PCE$. The line $BD$ meets $AC$ at $X$, and $CE$ meets $AB$ at $Y$.
Prove that $BX \leq CY$.