Puzzle #166: Date Puzzle 2

Consider a date in YYYY-MM-DD format. What is the closest, previous date where all eight digits were different?

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, August 10, 2016 at noon Pacific Time. I will post the answer shortly after.