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Elvis Presley was a famous singer from the 20th century. He had millions of fans who enjoyed listening to him sing and perform. When he would perform somewhere, his fans would be there to watch. Obviously, once Elvis had finished performing, he would leave the building, indicating that the show was finished. Today, this phrase is used to mean that something has reached completetion, or has ended.

Regarding this expression, Wikipedia mentions how it was used to disperse crowds after Elvis Presley concerts due to people lingering in hopes of seeing an encore. The first man believed to have used the phrase was Horace Lee Logan in 1956. Apparently, Elvis had just finished performing and was exiting the concert hall, so people were getting out of their seats to watch him leave. However, there were still more performances to be shown, so Logan announced:

"Alright, alright, Elvis has left the building. I've told you absolutely straight up to this point, you know that
he has left the building; he left the stage and went out the back with the policeman and he is now gone
from the building."

References: Wikipedia - Elvis Has Left The Building
Common Phrase Origins and Meanings > E-Letter Idioms
Find idioms and phrases with their meanings and history at Know Your Phrase!
* Jake went to the movies with his friends and after three long hours the movie had finally ended. Elvis had left the building and it was time to go home.
Origins for the idiom Drop Like Flies.
The meaning of the phrase Dropping Like Flies.
Said about things that have ended; finished.
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