Yes. Basically your proof tells us: if God exists, then God exists.
However there is one more subtlety here. Consider the general form:
- Nothing is X
- (1) is false because nothing cannot be anything
- Something is X
- X exists
I think there is a bit of a jump from 3 to 4. We could agree that faeries are something. We could also agree that they do not exist. In other words, the set of “somethings” is not restricted to the set of things that exist. Therefore, all things that exist are “something” but not all “somethings” exist.
We can go farther and ask what exactly is the set of “somethings” and I would say that they are the set of things for which we have necessary and sufficient conditions. So the argument becomes:
- Nothing has the necessary and sufficient conditions to be X
- (1) is false because nothing cannot have the necessary and sufficient conditions to be anything but nothing
- X has necessary and sufficient conditions
- X exists
Here we can see the flaw more clearly.