What is value of 1888 CC proof silver dollar?

At that time proof coins were only struck in Philadelphia, so you cannot have a proof coin from a branch mint. Further, coinage of silver dollars at Carson City was suspended in 1886 and not resumed until 1889.

Please check the coin again and post a new question with additional information. Unfortunately, you'll need to be prepared for the possibility that you have one of the many millions of fakes that have been pouring out of the Far East during the last couple of decades. Many of them are effectively fantasy pieces with impossible dates and/or mint marks (e.g. I saw a "Washington quarter" dated 1865!) but they can fool anyone who isn't up on all the details of mints and years.