Let $D$ be a point in the interior of $ABC$. Let $BD$ and $AC$ intersect at $E$ while $CD$ and $AB$ intersect at $F$. Let $EF$ intersect $BC$ at $G$. Let $H$ be an arbitrary point on $AD$. Let $HF$ and $BD$ intersect at $I$. Let $HE$ and $CD$ intersect at $J$ . prove that $G$,$I$ and $J$ are collinear