I booked a non-refundable roundtrip flight from IAH (Houston, Texas) to DEN (Denver, Colorado) with a connecting flight from DEN to RAP (Rapid City, SD) on the same day.

The problem is...I will already be in Denver on that day so I won't need to take the flight from IAH to DEN but I still need to fly to Rapid City

MY QUESTION:

If I don't take the flight from IAH to DEN will I still be allowed to take my flight from DEN to RAP?

Is there some law or airline policy that will prohibit me from taking the 2nd flight because I didn't take the first flight?

I sure would appreciate any input. Thanks!