Will I lose a building if a sell a prerequisite building

[Cosian]

For example, if I sell a police station in one of my cities after building The National Intelligence Agency, will I lose the National Intelligence Agency?

Or, in a single city, would I lose the Armory I build if I sell the Barracks?

 

[PreLynMax]

The short answer? No.
The longer answer? As long as you build it, and you don't sell, it, it won't go away.