Set Equality

Definition

$A=B$ iff every element of $A$ is in $B$ and every element of $B$ is in $A$ Either:$A=B\iff (A\subseteq B\wedge B\subseteq A)$ Or: $A=B\iff \forall x(x\in A\iff x\in B)$

Proving Equality

To prove $A=B$, prove that: $A\subseteq B$ and $B\subseteq A$