Class Equality is Symmetric

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

Let $=$ denote class equality.

Then:


 * $A = B \implies B = A$

Proof
From Biconditional is Commutative:


 * $\forall x: \left({ x \in A \iff x \in B }\right) \implies \forall x: \left({ x \in B \iff x \in A }\right)$

Hence the result by definition of class equality.