A double-lined bidirectional arrow representing logical equivalence or if-and-only-if relationships in mathematical logic and proofs.
Examples
Logical equivalence
A \Longleftrightarrow B \text{ means 'A if and only if B'}
Mathematical equivalence definition
x^2 = 4 \Longleftrightarrow x = 2 \text{ or } x = -2
Set equality condition
A = B \Longleftrightarrow (x \in A \Longleftrightarrow x \in B)