Logical equivalence

In logic, statements ${\displaystyle p}$ and ${\displaystyle q}$ are logically equivalent if they have the same logical content. This is a semantic concept; two statements are equivalent if they have the same truth value in every model (Mendelson 1979:56). The logical equivalence of ${\displaystyle p}$ and ${\displaystyle q}$ is sometimes expressed as ${\displaystyle p\equiv q}$, ${\displaystyle {\textsf {E}}pq}$, or ${\displaystyle p\iff q}$. However, these symbols are also used for material equivalence; the proper interpretation depends on the context. Logical equivalence is different from material equivalence, although the two concepts are closely related.

...
Wikipedia