The idiom existed many years before the rock anthem.
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For more: like a bat out of hell: Information from Answers.comlike a bat out of hell
Moving extremely fast, as in She ran down the street like a bat out of hell. This expression presumably alludes to the rapid darting movement of bats and, Charles Earle Funk theorized, their avoidance of such light as might be cast by the fires of hell. [c. 1900] For a synonym, see like greased lightning.
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