provided (that)
Assuming that; as long as it is true that; if it is the case that. I don't care if you wear headphones while you work, provided that it doesn't affect your productivity. I'd be happy to give you the information you're looking for, provided I get something in return, of course.
provided that
on the condition that. I will come, provided that I am invited. Iwill help you, provided that you pay me.