Left Right Arrow with Double Vertical Stroke

Left Right Arrow with Double Vertical Stroke at U+21FC denotes a bidirectional relation that is explicitly blocked, negated, or not valid in both directions. It belongs to the Arrows block, among specialized mathematical arrow symbols used to refine ordinary implication, mapping, and equivalence arrows. Its main use is in mathematical logic, set theory, and formal semantics, where a two-headed horizontal arrow normally suggests “if and only if,” mutual entailment, or a reversible correspondence, while the double vertical stroke marks that relation as failing. For instance, an author may use a barred left-right arrow between propositions to state that neither side is equivalent to the other, or that a claimed biconditional does not hold. It can also appear in theoretical computer science, algebra, and category-adjacent notation when writers need a compact negative form of a bidirectional mapping or transformation. In practice it is far less common than the plain left-right arrow, double arrow, or separately negated relation symbols, so many papers use it only after defining the notation locally.