\frac{\sin\angle{EAR}}{\sin\angle{RAF}}=\frac{ER}{RF}\cdot \frac{AF}{AE} \land \frac{\sin\angle{BAD}}{\sin\angle{DAC}}=\frac{BD}{DC}\cdot \frac{AC}{AB}\Leftrightarrow \frac{\sin\angle{EAR}}{\sin\angle{RAF}}=\frac{\sin\angle{BAD}}{\sin\angle{DAC}}\Longrightarrow \frac{BD}{DC}\cdot \frac{AC}{AB}=\frac{ER}{RF}\cdot \frac{AF}{AE}