Class Equality is Transitive

Theorem
Let $A$, $B$, and $C$ be classes.

Let $=$ denote class equality.

Then


 * $\left({ A = B \land B = C }\right) \implies B = A$

Proof

 * $\forall x: \left({ \left({ x \in A \iff x \in B }\right) \land \left({ x \in B \iff x \in C }\right) }\right) \implies \forall x: \left({ x \in A \iff x \in C }\right)$ by Universal Generalisation and Biconditional is Transitive