Problem #PRU-5120

Problem

In the triangle $ABC$ the lines $AE$ and $CD$ are the bisectors of the angles $\mathrm{\angle }BAC$ and $\mathrm{\angle }BCA$, intersecting at the point $I$. In the triangle $BDE$ the lines $DG$ and $EF$ are the bisectors of the angles $\mathrm{\angle }BDE$ and $\mathrm{\angle }BED$, intersecting at the point $H$. Prove that the points $B,H,I$ are situated on one straight line.