Axiom of separation The Axiom of separation states that, if A is a set then $\{a \in A ;\Phi(a)\}$ is a set.
Given a set $B \subseteq A$, Suppose I define $B=\{ a \in A ; a\notin B \}$.
This, of course leads to a contradiction. Because we define $B$ by elements not from $B$. My queation is: what part of the axioms sais that this kind of definition is not possible?
Thank you!

There is nothing at all to stop you defining a set $\Sigma$ such that $x \in \Sigma$ iff $x \in A \land x \notin B$, so $\Sigma = \{x \in A \mid x \notin B\}$. 
But what you've shown is that $\Sigma \neq B$! 
No problem so far.
What you can't do is then go on (having a knock-down argument to show that $\Sigma \neq B$) to assert, as you do, $\Sigma = B$. What could possibly legitimate that???
