A negated double-headed arrow indicating logical non-equivalence or absence of bidirectional implication between statements.
Examples
Logical non-equivalence
A \nLeftrightarrow B \text{ means 'A is not equivalent to B'}
Number theory relationship
p \text{ prime} \nLeftrightarrow p \text{ is Mersenne}
Set theory non-bijection
\mathbb{N} \nLeftrightarrow \mathbb{R} \text{ (not bijective)}