Equivalent

If $A\Rightarrow B$ and $B\Rightarrow A$ (i.e, $A\Rightarrow B\wedge B\Rightarrow A$, where $\Rightarrow$ denotes Implies), then $A$ and $B$ are said to be equivalent, a relationship which is written symbolically as $A\Leftrightarrow B$ or $A\rightleftharpoons B$. However, if $A$ and $B$ are ``equivalent by definition'' (i.e., $A$ is Defined to be $B$), this is written $A\equiv B$, a notation which conflicts with that for a Congruence.

See also Defined, Iff, Implies