Hey all. I started using bitcoin years ago. Stopped paying attention for a few years and now there are all these thin clients that people seem to recommend. I am unsure how they work.

Say I have some coins in Mycelium or Electrum or any other of these thin clients. Lets say something happens and the servers they use completely go away. How do I recover my coins? Is that possible? Do I not understand something?

Is there a tutorial somewhere that I can get at my bitcoins from one of these thin clients without EVER connecting to their servers? Like somehow get the wallet file out of them and slap it into a full client which does verify the whole chain and get my coins that way? I would like to do that myself before using/trusting one of these thin clients.