连接AFC,作FG∥BC交CD于点G,连接D1G,故AA1⊥BD,AC⊥BD,DE⊥GD1,A1D1⊥DE,故BD⊥面AA1C,DE⊥面A1GD1,又A1F在面AA1C和面A1FGD1上,故BD⊥A1F,DE⊥A1F,故A1F⊥面BDE.