1. Tooth fairy is defined as being maximally capable in stealth trading teeth for Dollar notes  (Definition applied).

2. If a being(Tooth Fairy) with the predicate of being maximally capable in stealth trading teeth for Dollar notes has not all possible tooth fairy trading skills, then it is not real Tooth Fairy (Premise 1)

3.  being maximally capable in stealth trading teeth for Dollar notes must applies it's skill on all lost teeth (Premise 2)

4.All lost teeth includes all known lost teeth (Modal logic necessity)

......... 5. It is possible that a Tooth Fairy exists (Assume for conditional proof, a.k.a no proof)

......... 6. Tooth Fairy will Stealth trade all possible teeth (Premise 3 and 5)

......... 7. Tooth Fairy will Stealth trade all know lost teeth (Premise 4 and 6)

8. If it is possible that a Tooth fairy exists, then a Tooth Fairy will Stealth trade allknown lost teeth (Conditional/no proof from Premises 5-7)

9. Impossibility is equivalent to not possible (By definition)

10. If something is not impossible, then it is not not possible (Premise 9)

11. Everything is either possible or impossible, though not necessarily necessary for possibility (Modal logic necessity)

12. Everything is possible unless impossible. (Premise 10 and 11)

13. Tooth Fairy has no contradicting features (Premise 1)

14. Tooth Fairy is not impossible (Premise 13)

15. Tooth Fairy is possible (Premise 12 and 14)

16. Tooth Fairy exists and takes care about all known lost teeth (Premise 8 and 15)