Yes, Alyosha, it's slang.
'ain't' means 'isn't'
There ain't no beer left. ('ain't' is often used in a double negative)
Ain't it nice?
Some people think it's common and shouldn't be used. In British English, however, it's used in a lot of dialects - but isn't accepted as intelligent conversation. Personally, I don't mind it (but I wouldn't teach my students to use it). Dialects are dialects and they're allowed to be different from the standard use.
You're right - 'ain't no denying' means 'there's no doubt, it's absolutely that way'.
We often use 'ain't' in song lyrics: "Ain't no sunshine when she's gone...."
As a teacher I'd say be aware of it so you understand it when you hear it, but it's probably best not to get into the habit of using it yourself.