I Do Not Exist

Inspired by an argument by Peter Unger:

Suppose that I exist. Then,
1. If I exist, then I am an animal.
2. If I am an animal, I am composed of a finite number of cells.
3. So if I exist, then I am composed of a finite number of cells.
4. For any cell of mine one might remove (which is not replaced by another cell), I will not cease to be me (that is, my identity is not so tenuous as to rely on being composed by any particular cell).
5. But then if 4 is true, then if you remove each cell, then I would not cease to be me.
6. If 5, then I would not cease to be. 
7. Thus, if all of my cells were removed, I would not cease to be.
8. HOWEVER, if one removed every cell composing me, then the animal which I am (according to 1) will cease to be (at some point in the cell removal process the animal will die).
9. But then we have a contradiction: If one were to remove all of my cells I would not cease to be (from 7) and I would cease to be (from 8, 1).
10. Thus what was supposed is false.
11. Thus, I do not exist.