Set is Small Class

Theorem

Let $x$ be a set.

Then $x$ is a small class.

Proof

$x = x$

Therefore by Existential Generalisation:

$\exists y: x = y$

$\blacksquare$

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Sources

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