Nothing is, therefore, given besides the understanding, by which several things may be distinguished one from the other, except the substances, or, in other words (see Ax.

iv.), their attributes and modifications.

Q.E.D.
PROP.V.There cannot exist in the universe two or more substances having the same nature or attribute.
Proof .-- 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 (Prop.

iv.).

If only by the difference of their attributes, it will be granted that there cannot be more than one with an identical attribute.