Implies sign

A double-shafted arrow pointing right, denoting logical implication.

Also known as: Material implication, Double arrow

MathematicalScientificStandard profile

Meanings

⇒ denotes implication: if the left statement holds then so does the right. It does not claim the two are equivalent, and reading it as 'means the same as' is the commonest error made with it.

Officially standardisedVerified fact
Is encoded as U+21D2 RIGHTWARDS DOUBLE ARROW, in the Arrows block rather than among the mathematical operators.
Contexts: Mathematics
Common modern usageVerified fact
States that if the statement on its left holds, then so does the statement on its right.
Contexts: Mathematics
Common modern usageVerified fact
Is one-directional: it makes no claim that the right statement implies the left, which is what the double-headed form asserts instead.
Contexts: Mathematics

Visual description

An arrow pointing to the right whose shaft is drawn as two parallel horizontal lines, ending in a single open head.

Symmetry: horizontal
Orientation: upright

Commonly confused with: Reaction arrow
Both are rightward arrows asserting that one thing follows from another.
Commonly confused with: If-and-only-if sign
One direction against both; the difference is a second arrowhead.
Commonly confused with: Arrow function notation
The double-stroke rightward arrow is shared: one asserts that a statement follows from another, the other introduces a function.

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 implication: if the left statement holds then so does the right. It does not claim the two are equivalent, and reading it as 'means the same as' is the commonest error made with it.

Officially standardisedVerified fact

Is encoded as U+21D2 RIGHTWARDS DOUBLE ARROW, in the Arrows block rather than among the mathematical operators.

Contexts: Mathematics

Common modern usageVerified fact

States that if the statement on its left holds, then so does the statement on its right.

Contexts: Mathematics

Common modern usageVerified fact

Is one-directional: it makes no claim that the right statement implies the left, which is what the double-headed form asserts instead.

Contexts: Mathematics

Related & commonly confused symbols

Commonly confused with: Reaction arrow
Both are rightward arrows asserting that one thing follows from another.
Commonly confused with: If-and-only-if sign
One direction against both; the difference is a second arrowhead.
Commonly confused with: Arrow function notation
The double-stroke rightward arrow is shared: one asserts that a statement follows from another, the other introduces a function.

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