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Here is an example of Proposition 6.  The black circle is level one, the white circle is level two, and the black square is level three.

Proposition 6: One substance cannot be produced by another substance.

• Prop. 5: In nature there cannot be two substances of the same attribute
  • If there were two or more distinct substances, they would have to be distinguished from one another by difference of attributes or difference of modifications. Prop. IV
    • Everything which exists, exists either in itself or in something else. Axiom I
    • There is nothing outside of the intellect but substances and their modifications. Defs. III and V
    • An attribute is that which the intellect perceives of substance as constituting its essence. Def. IV
    • So, there is nothing outside the intellect by which a number of things can be distinguished one from another but substance, or, in other words, their attributes and their modifications
  • If only by the difference of their attributes, it will be granted that there cannot be more than one with an identical attribute.
  • So there cannot be two or more distinct substances having the same attribute that are distinguished from one another by different attributes.
  • Substance is prior by nature to its modifications. Prop. I
    • Since a modification is that which is in another thing through which also it is conceived. Def. V, and a substance does not need the conception of another thing Def. III, then substance is prior by nature to its modifications.
  • Since substance is prior by nature to its modifications, two substances cannot be distinguished by a difference in modifications.

• Two substances having different attributes have nothing in common with one another. Prop. 2
  • Each substance must be in itself and must be conceived through itself, that is to say, the conception of one does not involve the conception of the other. Def. III
  • So two substances having different attributes have nothing in common with one another.
• If two things have nothing in common with one another, one cannot be the cause of the other. Prop. 3.
  • If two things have nothing in common with one another, they cannot through one another be mutually understood. Axiom V
  • But the knowledge of an effect depends on and involves the knoweldge of the cause. Axiom IV
  • So things with nothing in common cannot be understood through each other and cannot be the cause of each other.
• So one substance cannot cause another.