Why is Macduff able to kill Macbeth despite the prophecy?

The witches prophesied that Macbeth would only be defeated when "Birnam Wood comes to Dunsinane." Macduff was able to kill Macbeth despite this prophecy because he used branches from Birnam Wood to camouflage his army as they approached Dunsinane. As a result, Macbeth believed that the forest was moving, which fulfilled the prophecy and allowed Macduff to defeat him.