What is the proper usage of "not to mention"/let alone?

What is the proper usage of "not to mention/“let alone”?

Should I list the least the obvious and end with the most obvious.

  1. "Paris is a world famous city, an oasis of fine dining, an international tourist mecca, not to mention the capital of France.

  2. "Your mother would never allow you to travel to London on your own, never mind/let alone give you the money to travel there.

From reading many examples I get the impression that the rules for its usage (which I’m not even sure of) are loosely or never followed, hence my confusion.

I look forward to your feedback.

They’re idioms that signify that I’ve clearly made my point with the first part of the list without needing the smoking gun that is the last point, but I’m going to mention it anyway so you know that I am aware of it and didn’t simply forget it.

Thanks InnerStickler. That’s how I understood it too.