Ordered Pair

Last updated Nov 1, 2022

Let $x, y$ be two Sets. Then the Ordered Pair $(x, y)$ is defined as the Set ${{x}, {x, y}}$.

${x, y}$ exists as per the Axiom of Pairing. ${x}$ exists as well as per the Axiom of Pairing (pairing $x$ and $x$). Thus ${{x}, {x, y}}$ exists as per the Axiom of Pairing. $\blacksquare$