Enchanted permanent is indestructible. (Effects that say "destroy" don't destroy that permanent. An indestructible creature can't be destroyed by damage.)
Illus. Darrell Riche
10/1/2009: Lethal damage, damage from a source with deathtouch, and effects that say "destroy" won't cause an indestructible permanent to be put into the graveyard. However, an indestructible permanent can be put into the graveyard for a number of reasons. The most likely reasons are if it's sacrificed, if it's legendary and another legendary permanent with the same name is on the battlefield, if it's a planeswalker and another planeswalker with the same subtype is on the battlefield, if it's a creature with toughness 0 or less, or if it's an Aura that's either unattached or attached to something illegal.
10/1/2009: If an effect would simultaneously destroy Indestructibility and the creature it's enchanting, only Indestructibility is destroyed.
10/1/2009: If a creature enchanted by Indestructibility is dealt lethal damage, the creature isn't destroyed, but the damage remains marked on the creature. If Indestructibility stops enchanting that creature later in the turn, the creature will stop being indestructible and will be destroyed.
Magic 2010
(Rare)