Axiom:Axiom of Pairing

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Set Theory

For any two sets, there exists a set to which only those two sets are elements:

$\forall a: \forall b: \exists c: \forall z: \paren {z = a \lor z = b \iff z \in c}$

Class Theory

Let $a$ and $b$ be sets.

Then the class $\set {a, b}$ is likewise a set.

Also known as

The Axiom of Pairing is also known as the Axiom of the Unordered Pair.

Some sources call it the Pairing Axiom.

Also see

  • Results about the axiom of pairing can be found here.