Why is it that if 2+2=3 then unicorns exist?

I don't think this puzzle has anything in particular to do with "formalness" of logic. Here is a short non-formal argument. It is strange that we seem to need an argument for something so simple, but it seems we (at least I) do. Some persons find it so strange as to be paradoxical -- I do not. (sfa)
  1. If 2+2=3, then (2+2=3 or unicorns exist).

  2. If 2+2=3 or unicorns exist then unicorns exist. (since not 2+2 = 3)

  3. If 2+2=3 then unicorns exist. (by chaining 1 and 2)
Here's the same argument with some more general comments added:
  1. If 2+2=3, then (2+2=3 or unicorns exist).

    [since generally, if P then (P or Q) ; Or to paraphrase, if the first of two claims is true, then at least one of the two claims is true.]

  2. If 2+2=3 or unicorns exist then unicorns exist.

    [since not 2+2 =3, and generally, if not P, then if P or Q then Q ; Or again, if the first of two claims is false, but at least one of the two claims is true, then the second one is true.]

  3. If 2+2=3 then unicorns exist. (by chaining 1 and 2)

    [And so generally, if the first of two claims is false, then the second one, whatever it is, would follow by this form of argument from the erroneous assumption that the first one was true.]

Some readers might find the proof makes a different impression by using (17 evenly divides 1308) instead of 2+2=3.