证明：因为$E$是$\triangle ABC$的内心，所以$\angle BAD = \angle CAD，$$\angle ABE = \angle CBE。$因为$\angle CAD = \angle CBD，$所以$\angle BAD = \angle CBD。$因为$\angle BED = \angle BAD + \angle ABE，$$\angle EBD = \angle CBD + \angle CBE，$所以$\angle BED = \angle EBD，$所以$BD = DE。$
