How does Spinoza deduce substance must cause itself?

Question

Prop. VII. Existence Belongs to the Nature of Substance

Spinoza demonstrates this by arguing substance must be the cause of itself, i.e. existence must belong to the nature of substance (by def. 1). In doing so, he references only the corollary of Prop. VI., which states that substance cannot be produced by anything else. From what I can tell, this does not preclude a substance not existing. I feel there is an assumed “if it exists” preceding Prop. VII., though I don’t doubt it may be possible how it is written is correct and can be arrived at following what’s written prior in Part I. Can anyone provide insight on how Spinoza arrived at the claim that substances must cause themselves rather than not exist at all?

Note: Spinoza makes another argument in the second scholium of Prop. VIII. for the essential existence of substance, but from what I can tell, this is similarly based upon the absurdity of substance being created and does not mention the case where substance doesn’t exist.

Answer 1

Implicit in Spinoza's argument is that stuff actually exists. This was proven by Descartes when he said "I think therefore I am". At the very least, I exist, so stuff actually exists.

If stuff actually exists, then that which exists must have as its basis substance which will have existence as its essence.

Here is the argument as I understand it:

(1) One substance cannot be caused by another substance.

This follows from the definition of a substance since two different substances can have nothing in common.

(2) Existence belongs to the nature of substance

This follows that a substance cannot be caused by another substance.

(3) Therefore, existence must be self-caused

If existence belongs to the nature of a substance and a substance cannot be caused by another substance, it must be, by Spinoza's first definition: "self-caused"

Here is a link to the Project Gutenberg Elwes translation of Ethics.