Substitution of Elements

Theorem
Let $a$, $b$, and $x$ be sets.


 * $( a = b \implies ( a \in x \iff b \in x ) )$

Proof
By the Axiom of Extension, $( a = b \implies ( a \in x \implies b \in x ) )$

Equality is Symmetric, so also by the Axiom of Extension, $( a = b \implies ( b \in x \implies a \in x ) )$