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Now you can reattach the external drive, on which you should see a folder called "OS X Install Data" that contains a disk image file called InstallESD.dmg. With the drive unplugged, your Mac will boot normally to its internal drive.
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When your Mac automatically restarts, it will display a black screen with no video output for a second or two.
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The copy of OS X that is included with your Mac is not considered a retail purchase, so unfortunately you will be able to access it only through Apple's installer. However, this requires you to purchase a separate license of OS X. One easy option (which I have discussed before) is to purchase OS X from the App Store, then create a boot drive from its contents.
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Granted, the use of Time Machine makes restoring from backup relatively easy, but if for some reason you need to repartition the hard drive or install a new one on your system, you will first need to install OS X again. While convenient for those with fast broadband connections, sometimes you may find yourself in a location without fast Internet and would benefit from having a way to reinstall OS X from scratch. Instead, if you wish to reinstall OS X you simply reboot to the OS X Recovery HD and use the tools there to format your hard drive (should you choose to), then run the installer to download OS X from Apple's servers. Since its move to online purchasing and distribution of its operating system software, Apple has no longer included gray recovery DVDs with its Mac systems.
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