# Pair is Union of Singletons

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## Theorem

Let $x, y$ be arbitrary.

Then $\left\{ {x, y}\right\} = \left\{ {x}\right\} \cup \left\{ {y}\right\}$

## Proof

Straightforward from Union of Unordered Tuples.

$\blacksquare$

## Sources

- Mizar article ENUMSET1:1