The Components of an Ordered Pair

In the setting of Class Theory NBG: the Axioms, Standing Conventions and Basic Notation, let $p$ be an ordered pair.

¶ The first and second components of $p$, as in The Ordered Pair of Two Sets and Nested Tuples §pair, are written $p_{1}$ and $p_{2}$: $p_{1}$ is the unique set $z$ with $\exists y\,(p=(z,y))$ and $p_{2}$ the unique set $z$ with $\exists x\,(p=(x,z))$, unique by The Characteristic Property of Ordered Pairs and Nested Tuples of Sets §characteristic. They are defined set symbols, used for ordered pairs $p$.