   \(A\) is \(a\) if and only if ((for some \(B, B\) is \(A)\) and (for any \(B\) and \(C\), if \(B\) is \(A\) and \(C\) is \(A\), then \(B\) is \(C)\), and (for any \(B\), if \(B\) is \(A\) then \(B\) is \(a))\)  