tax break for trade in? Trading my car for used car?

I am about to trade in my truck for a used car. I owe $20,000 on my car and the dealer is going to give me $20,000 for it. The car I am buying is $16,000. The dealer said that I do not have to pay tax because I am trading in my truck. Is this true? He said it is one of the benefits of trading in a high value car for a lower priced car. Any insight into this would be greatly appreciated!