If-and-only-if sign

A double-shafted arrow with heads at both ends, denoting logical equivalence.

Also known as: Iff, Double-headed arrow

MathematicalScientificStandard profile

Meanings

⇔ denotes equivalence: each statement implies the other. The second arrowhead is the whole difference from one-directional implication, and it is the difference between 'if' and 'if and only if'.

Officially standardisedVerified fact
Is encoded as U+21D4 LEFT RIGHT DOUBLE ARROW, in the Arrows block.
Contexts: Mathematics
Common modern usageVerified fact
States that each of the two statements implies the other, so they hold in exactly the same circumstances.
Contexts: Mathematics
Common modern usageVerified fact
Is abbreviated 'iff' in written mathematics, a deliberate doubling of the f to distinguish equivalence from the one-directional 'if'.
Contexts: Mathematics

Visual description

A horizontal arrow whose shaft is drawn as two parallel lines, with an open arrowhead at each end.

Symmetry: horizontal
Orientation: upright

Commonly confused with: Resonance arrow
Both are double-headed arrows between two expressions, in unrelated fields.
Commonly confused with: Implies sign
Both directions against one; the second head is the difference.

Confidence

IdentityHigh confidence: High confidence because the identity is defined by a current official standard, but multiple independent sources agree.
Historical originModerate confidence: Moderate confidence because the historical origin is documented in encyclopedic references, but multiple independent sources agree, but early or supporting evidence is limited, but the regional or cultural match to this specific claim is not precise.
Current useHigh confidence: High confidence because the current use is defined by a current official standard, but multiple independent sources agree.
Visual matchHigh confidence: High confidence because the visual match is documented in encyclopedic references, but multiple independent sources agree.

Sources

Unicode Code Chart: Arrows (U+2190–U+21FF)
The Unicode Consortium · retrieved 2026-07-31
Authoritative for the character's code point, name and block only. Unicode assigns identity; it does not define what a symbol means in use.
Glossary of mathematical symbols
Wikipedia · retrieved 2026-07-31
Tertiary reference. Used for what the notation means in ordinary mathematical practice and for attribution of its introduction, not for a claim that any body defines it.
Logical connective
Wikipedia · retrieved 2026-07-31
Tertiary reference. Used for what the notation means in ordinary mathematical practice and for attribution of its introduction, not for a claim that any body defines it.
Unicode Code Chart: Mathematical Operators (U+2200–U+22FF)
The Unicode Consortium · retrieved 2026-07-30
Authoritative for the character's code point, name and block only. Unicode assigns identity; it does not define what a symbol means in use.

Last reviewed 2026-08-01

Part of

Set theory and logic notation

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Meanings

⇔ denotes equivalence: each statement implies the other. The second arrowhead is the whole difference from one-directional implication, and it is the difference between 'if' and 'if and only if'.

Officially standardisedVerified fact

Is encoded as U+21D4 LEFT RIGHT DOUBLE ARROW, in the Arrows block.

Contexts: Mathematics

Common modern usageVerified fact

States that each of the two statements implies the other, so they hold in exactly the same circumstances.

Contexts: Mathematics

Common modern usageVerified fact

Is abbreviated 'iff' in written mathematics, a deliberate doubling of the f to distinguish equivalence from the one-directional 'if'.

Contexts: Mathematics

Confidence

IdentityHigh confidence: High confidence because the identity is defined by a current official standard, but multiple independent sources agree.
Historical originModerate confidence: Moderate confidence because the historical origin is documented in encyclopedic references, but multiple independent sources agree, but early or supporting evidence is limited, but the regional or cultural match to this specific claim is not precise.
Current useHigh confidence: High confidence because the current use is defined by a current official standard, but multiple independent sources agree.
Visual matchHigh confidence: High confidence because the visual match is documented in encyclopedic references, but multiple independent sources agree.

Sources

Unicode Code Chart: Arrows (U+2190–U+21FF)
The Unicode Consortium · retrieved 2026-07-31
Authoritative for the character's code point, name and block only. Unicode assigns identity; it does not define what a symbol means in use.
Glossary of mathematical symbols
Wikipedia · retrieved 2026-07-31
Tertiary reference. Used for what the notation means in ordinary mathematical practice and for attribution of its introduction, not for a claim that any body defines it.
Logical connective
Wikipedia · retrieved 2026-07-31
Tertiary reference. Used for what the notation means in ordinary mathematical practice and for attribution of its introduction, not for a claim that any body defines it.
Unicode Code Chart: Mathematical Operators (U+2200–U+22FF)
The Unicode Consortium · retrieved 2026-07-30
Authoritative for the character's code point, name and block only. Unicode assigns identity; it does not define what a symbol means in use.

Last reviewed 2026-08-01

Meanings

Visual description

Related & commonly confused symbols

Meanings

Visual description

Related & commonly confused symbols