To prove that there exists a unicorn, it’s enough to prove the stronger proposition that there exists an existing unicorn. (An “existing unicorn” is just a unicorn which exists.)
For, obviously, if there exists an existing unicorn, then there must exist a unicorn!
So all we have to do is prove that an existing unicorn exists. But that’s not very hard. How could an existing unicorn not exist? That would be a contradiction!"