No it is not. Your logic and language are faulty. Here is how this breaks down. With all your philosophy, you have forgotten how to see things simply.
To first use another example, this is what I said:
An apple is a fruit.
A fruit is the ripened seed-bearing part of a plant when fleshy and edible.
An apple is the ripened seed-bearing part of a plant when fleshy and edible.
If that were the case, then you'd be giving an incorrect definition of apple. You see, when you are making a stipulative definition like that, you are supposed to be offering necessary and sufficient conditions for the thing in question, otherwise it is not a definition. The definition of an apple is *not* "the ripened seed-bearing part of a plant when fleshy and edible", because although that is a *necessary* condition on apple-hood, it is not a sufficient condition: there can be ripened seed-bearing parts of plants that are fleshy and edible, yet aren't apples. If you don't understand what it is to give a definition, that aint my problem!
You think that I said
An apple is a fruit.
A fruit is the ripened seed-bearing part of a plant when fleshy and edible.
therefore:
The ripened seed-bearing part of a plant when fleshy and edible is the ripened seed-bearing part of a plant when fleshy and edible.
No, I don't think you said that. The statement "an apple is a fruit" is not a definition of an apple. You're equivocating on the word "is" in your alleged analogy!
God alone is
Is = exists
therefore: god alone exists
Exists = that which is infinite, eternal, unchanging, and permanent
therefore: God is that which is infinite, eternal, unchanging, and permanent
Again, you seem to be equivocating! When you say "exists = that which is infinite..." then you seem to be offering a genuine definition. But when you then infer "God is that which is infinite..." from your assumption that God alone is, you are not defining God, you are simply making an inference of this sort:
1. God exists (starting assumption)
2. "Exists" is defined as "that which is infinite, eternal, unchanging, and permanent"
3. Therefore, God is infinite, unchanging, eternal, and permanent.
Now, even if I grant you that starting assumption, all that you've done is prove that God exemplifies the properties of being infinite, unchanging, eternal, and permanent. You haven't defined God at all! You've just said "God exists, and something that exists has such and such properties, so God has such and such properties". I hope you can see how this isn't a
definition of God!
So I ask again: How do you
define the term "God"?
"God alone exists" is just a statement. By defining "exists" I am not creating a tautology or affirming the laws of identity, just pinning down for the reader what "exists" means and substituting it in the statement. You seem to be trying to twist this into a philosophical "argument" where strange laws of logic rule.
I'm not even sure what the heck you are trying to say here, so I'll just ask this. How precisely is what you are doing different than the following dialogue:
Grimace: God alone is

Hamburgler: Hey Grimace! Interesting thesis! I wonder, though, how do you define the term "God"?
Grimace: "God" = That which is a cheeseburger.
Hamburgler: Cool! So, my next question is, how do you define the term "exist"?
Grimace: "exist" = That which is a cheeseburger.
Hamburgler: So, plugging in your definitions, when you say "God alone is" you are saying "That which is a cheeseburger alone is a cheeseburger"?
Hamburgler: No! um... (mutters something about apples)
The illogic of the old "God is love, love is blind, Ray Charles is blind, therefore RC is god" is not present either. In my statement the subject of the sentence is always "god" and it is only the description of "god" that changes. Mathematically I just did this:
10 = (5+5) God (10) = alone is/exits (5+5)
(5+5) = (3+7) exists (5+5) = that which is... (3+7)
10 = (3+7) god (10) = that which is (3+7)
I have absolutely no idea what you are saying here.
It is not meant to be profound. It is just a statement of an underlying assumption. It is not unlike saying that "the universe is all that exists". Maybe you consider that profound. I don't. It is merely a position statement. Now such statements are very important to understanding they way people think about things, but they are not particularly profound.
Its very far from profound! It's not the least bit interesting. It's not an assumption either, its a necessary truth! It's the exactly analogous to saying "a water bottle is a watter bottle" or "a chair is a chair".
Perhaps you know what moves people to find meaning (=profundity) in words and are an expert on what is meaningful and what is not. You certainly have taken it upon yourself to be my most vocal critic of what is meaningful and what is not.
Meaning is not the same thing as profundity! When I used the word meaning, I roughly meant "of any interest to anyone". When your definitions are tantamount to affirming a trivially true identity claim, they are absolutely uninteresting! I don't just mean that as someone who doesn't share your "worldview". They are as uninteresting as saying "I'm going to start my world view with the assumption that a water bottle is a water bottle".