Q.E.D.
Corollary .-- Hence it follows that a substance cannot be produced by anything external to itself.

For in the universe nothing is granted, save substances and their modifications (as appears from Ax.i.and Deff.iii.

and v.).

Now (by the last Prop.) substance cannot be produced by another substance, therefore it cannot be produced by anything external to itself.
Q.E.D.

This is shown still more readily by the absurdity of the contradictory.