Def/Ordered pair



Generally, given a set $p$, we say that $p$ is an ordered pair if: $$\exists x, \exists y \mbox{ such that } p = \{ \{ x \}, \{ x,y \} \}.$$

If $p$ is an ordered pair, then the first and second entries of $p$ can be defined as follows:
 * $x$ is the first entry of $p$ iff $\forall e \in p, x \in e$.
 * $y$ is the second entry of $p$ iff $(\exists! e \in p, y \in e)$.

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