No two substances can share an attribute
Formal Statement
There cannot exist in nature two or more substances having the same attribute. If two substances shared an attribute, they could not be distinguished by that attribute; and since substance is prior to its modifications (P1), they could not be distinguished by their modes either. Therefore they would be indistinguishable — which means they are not really two.
In Plain Language
Spinoza is closing the door on substance plurality within any single attribute. Suppose you claim there are two substances that are both "extended." How would you tell them apart? Not by the attribute they share, and not by their modes, because substance is more fundamental than any mode. If you cannot distinguish them, you do not have two substances — you have one. This is a crucial bottleneck on the road to monism.
Why This Follows
From P1 (gs-06) we know substance is prior to its modifications. From Def.3 (gs-01) and Def.4 (gs-02), each substance is conceived through itself via its attributes. If two substances shared the same attribute, neither their attribute nor their modes (which are posterior) could distinguish them, making them identical — not genuinely two.
Within any given attribute, there can be at most one substance.
Could two substances share some attributes but differ in others? What would Spinoza say?