# Set is Small Class

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## Theorem

Let $x$ be a set.

Then $x$ is a small class.

## Proof

- $x = x$

Therefore by Existential Generalisation:

- $\exists y: x = y$

$\blacksquare$

## Sources

- 1971: Gaisi Takeuti and Wilson M. Zaring:
*Introduction to Axiomatic Set Theory*: $\S 4.11$