# Class Equality is Reflexive

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## Theorem

Let $A$ be a class.

Then:

- $A = A$

where $=$ denotes class equality.

## Proof

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- $\forall x: \left({ x \in A \iff x \in A }\right)$

$\blacksquare$

## Sources

- 1971: Gaisi Takeuti and Wilson M. Zaring:
*Introduction to Axiomatic Set Theory*: $\S 4.7 \ (1)$