I was thinking about the question "Why is there something rather than nothing?" , and have read about some theories that existence is the case because non-existence is logically impossible
So, I devised a logical proof that shows nothingness is impossible, but only if we can formally denote nothingness by : "There exists x, so that for all y , y is not identical to x".
Which violates the law of identity, therefore : nothingness is logically impossible. (there is no x that is not identical to all y)
My question : are there any references that try to denote "nothingness" in formal terms?