21. Proof that unicorns exist

I wish to prove to you that there exists a unicorn.

To do this, it obviously suffices to prove the (possibly) stronger statement that there exists an existing unicorn. (By an existing unicorn I of course mean a unicorn which exists.) Surely if there exists an existing unicorn, then there must exist a unicorn.

So all I have to do is prove that an existing unicorn exists.

Well, there are exactly two possibilities:

(1) An existing unicorn exists.
(2) An existing unicorn does not exist.

Possibility (2) is clearly contradictory: How could an existing unicorn not exist? Just as it is true that a blue unicorn is necessarily blue, an existing unicorn must necessarily be existing.