Definition
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[1Y3] Axiom of pairing. Given any two sets \(X\) and \(Y\) there exists a set \(Z\), denoted by \(Z=\{ X,Y\} \), whose only two elements are \(X\) and \(Y\). In formula
\[ β X, Y β Z : β W (W β Z) \iff (W = X) β¨ (W = Y )\quad . \]
Again, by the axiom of extensionality [1Y8], the set \(Z\) unique.