证明：∵四边形ABCD是平行四边形，∴AD∥BC，AB=CD，∴∠AFB=∠CBF，∠DEC=∠BCE，∵BF平分∠ABC，CE平分∠BCD，∴∠ABF=∠CBF，∠DCE=∠BCE，∴∠ABF=∠AFB，∠DCE=∠DEC，∴AB=AF，DE=CD，∴AF=DE，∴AE=DF．
