For, if substance be produced by an external cause, the knowledge of it would depend on the knowledge of its cause (Ax.

iv.), and (by Def.

iii.) it would itself not be substance.
PROP.VII.

Existence belongs to the nature of substances.
Proof .-- Substance cannot be produced by anything external (Corollary, Prop vi.), it must, therefore, be its own cause--that is, its essence necessarily involves existence, or existence belongs to its nature.
PROP.VIII.

Every substance is necessarily infinite.
Proof .-- There can only be one substance with an identical attribute, and existence follows from its nature (Prop.