Proof.- (5:1) If several distinct substances be granted, they must be
distinguished one from the other, either by the difference of their
attributes, or by the difference of their modifications ([iv] ). (2) If
only by the difference of their attributes, it will be granted that
there cannot be more than one with an identical attribute. (3) If by
the difference of their modifications, as substance is naturally prior
to its modifications ([i] ), it follows that setting the modifications
aside, and considering substance in itself, that is truly; ([D.iii] and
[D.vi] }, there cannot be conceived one substance different from another,
that is (by [iv] ), there cannot be granted several substances, but
one substance only. Q.E.D.
PROP. [VI] One substance cannot be produced by another substance.
Proof.- (6:1) It is impossible that there should be in the universe two
substances with an identical attribute, i.e. which have anything common
to them both ([ii] ), and, therefore ([iii] ), one cannot be the cause of
another, neither can one be produced by the other. Q.E.D.
Corollary.- (6:2) Hence it follows that a substance cannot be produced by
anything external to itself. (3) For in the universe nothing is granted,
save substances and their modifications (as appears from [A.i] and [D.iii]
and [D.v] ). (4) Now (by [v] ) substance cannot be produced by another
substance, therefore it cannot be produced by anything external itself.
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