Do unicorns exist?

I am going to prove to you that there exists a unicorn. To do this I have to prove the (possibly) stronger statement that there exists an existing unicorn. (By an existing unicorn I of course mean one that exists.) Surely if there exists an existing unicorn, then there must exist a unicorn. So all I have to do is... show more I am going to prove to you that there exists a unicorn. To do this I have to prove the (possibly) stronger statement that there exists an existing unicorn. (By an existing unicorn I of course mean one that 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.
Update: lol its just a paradox don't all have a go at me. Anyway how do you know if you've never met one, they might just be shy...
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