Learn Dutch: We zijn zo opgelucht dat er geen probleem is. - We are so relieved that there is no problem.

The word dat (that) is a subordinating conjunction. In Dutch, subordinating conjunctions push the verb to the end of their clause. Here, dat er geen probleem is is a subordinate clause showing the result of being zo opgelucht (so relieved).

Does zo ... dat always work like "so ... that" in English?

Yes! You can use zo followed by an adjective or adverb, and then dat to express a result. For example, "so cold that..." is zo koud dat.... Just remember that the dat half of the sentence will always use verb-final word order.

Why do we use er here instead of just saying dat is geen probleem?

The phrase er ... is is the Dutch equivalent of "there is" (often called the existential er). If you said dat is geen probleem, it would mean "that is not a problem" rather than "there is no problem."

Could I say niet een probleem instead of geen probleem?

No, you should use geen. In Dutch, when you negate a noun that uses "a" or "an" (an indefinite noun like een probleem), you always use geen (no / not a) instead of niet een.