Existence belongs to the nature of substance
Formal Statement
Existence belongs to the nature of substance. Since substance cannot be produced by anything external (P6, Corollary), it must be its own cause — its essence necessarily involves existence. To conceive of substance at all is already to conceive of it as existing.
In Plain Language
Here is where substance gets its extraordinary status. Because nothing outside it can bring it into being (gs-08), and because it does exist (or else we could not be talking about it), its existence must come from its own nature. This is not a trick — it follows from the conceptual self-sufficiency built into the definition. If substance depended on something else for existence, it would be conceived through that something else, and then it would not be substance. So substance just is the kind of thing that exists by its own nature.
Why This Follows
From P6 and its corollary (gs-08), substance cannot be produced by anything external. By the definition of substance (gs-01), it is conceived through itself. Its existence, then, must be grounded in its own nature — there is nowhere else for that ground to come from.
Substance exists necessarily; its essence involves existence.
Is this an ontological argument, and if so, does its validity depend on accepting Spinoza's definitions?