I don't quite get that since you obviously at one point have tested a defined God and found that it is unsustainable by your use of the principle. You have therefore used the principle before. Since I have no experience of it's use the best exemplar is the one you have already used and it is fitting in my view that you go through it. No, the start is for you to give your example of how you used it to confidently suggest that God is non existent surely?
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My reply in the other thread was to Outrider, and I am fairly confident that I understand Outrider's vocabulary and indeed the context from which he posed the question. In case of misunderstanding he could have queried my reply.
The principle itself is well explained in wiki, even a proof is provided. There are also various other names, formulations possible, it is a well known tautology in classical logic.
So, in the context assumed by me to be shared with Outrider, for something to "exist" means that the something has objective reality (being). Claims can be made and verified (or not) on the properties or behaviour of the something. In this context there is no objective "God" about which we can verify or reject any claims, so by, the logical tautology, we can make any claims we choose in full confidence.
I am not confident that "God" does not exist at all - but there is certainly no such object in the context of the empirical scientific model/language - in which "God" remains mostly undefined but, if existent, would have objectively verifiable/falsifiable properties.