Class Equality is Symmetric

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Let $A$ and $B$ be classes.

Let $=$ denote class equality.


$A = B \implies B = A$



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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.