How do I prove that $A\subseteq (A \times A)\rightarrow A = \varnothing$ in axiomatic set theory?
This is theorem 107 of Patrick Suppes "Axiomatic Set Theory". I do not buy his argument that the set $A$ does not contain any empty sets because, according to him, the set $A$ is a subset of $A\times A$. Are there any other arguments that prove this theorem? Why does the set $A$ not have the empty set as a member?