Implies (⇒): Meaning, Examples & LaTeX

Semantic identity and intent

Semantic type

operator

An operator, relation, connective, or notation mark whose meaning depends on its operands and context.

Primary search task

understand the operation or relation, see a valid example, and copy the correct notation

Logic SymbolsArrows

MathML token

<mo>

Use ⇒ with the operand structure shown in the examples. Preserve grouping, limits, spacing, and evaluation order when converting between formats.

Characters to distinguish

⇔ — If and Only If
→ — Right Arrow

Use ⇒ in the right format

Open LaTeX Convert format Search related notation

Meaning and usage

Indicates logical implication from a premise to a conclusion.

Use it between complete statements; do not treat it as ordinary equality.

Pronunciation: implies

Formula examples

x>2\Rightarrow x>0

How to type Implies

Windows: Use Character Map or enter U+21D2 in a Unicode-aware app.
macOS: Open Character Viewer with Control–Command–Space and search by name.
Microsoft Word: Type \Rightarrow in an equation and press Space.
iPhone and iPad: Copy and paste ⇒, or use a math/LaTeX app. The standard iOS keyboard may not expose every mathematical symbol.
Android: Copy and paste ⇒, or use a math keyboard or LaTeX editor. Keyboard layouts vary by device and app.
Google Docs: For plain text, paste ⇒ or use Insert → Special characters. For structured math, use the equation editor and verify \Rightarrow.
Excel: Paste ⇒ into a cell or use Insert → Symbol when available. Ordinary cells preserve the character but do not interpret LaTeX commands.

Common mistakes

Define the logical convention before using ⇒; proof, programming, and Boolean-algebra sources may assign different precedence or direction.
For plain text, copy ⇒ as U+21D2; for structured equations, use \Rightarrow in math mode. A look-alike glyph or image can break search, accessibility, or parsing when the intended character is Implies.

When to use ⇒

Use ⇒ in plain text when a Unicode character is appropriate and the destination preserves U+21D2.
Use \Rightarrow in an equation editor when mathematical spacing or structure matters.
Define the local meaning when Implies is used in logic, arrows with a field-specific convention.

Look-alikes and related characters

⇔ — If and Only If
→ — Right Arrow

Font and compatibility notes

Glyph shape can vary by font. Verify the code point after copying, and prefer LaTeX or MathML for structured equations.

Continue the workflow

From Implies to a finished equation

Copy the characterUse ⇒ in plain text when Unicode is accepted.
Choose a structured formatUse \Rightarrow for LaTeX or the MathML snippet for accessible web equations.
Edit or convertOpen the value in the editor or converter without retyping it.

Continue in editor Read a related guide Open cheat sheet

Review and source notes

Quality tier: core

Last reviewed: 2026-07-26

Review method: Checked Implies against its Unicode identity, LaTeX representation, HTML serialization, MathML token, and copy-and-paste behavior.

Verified against: Unicode Standard, Unicode mathematical notation guidance, and established LaTeX/MathML syntax.

Reference sources

The Unicode StandardUnicode Consortium — Character identity, encoding, names, and conformance.
Unicode Character Code ChartsUnicode Consortium — Code points and official character charts.
Unicode Technical Report #25: Unicode Support for MathematicsUnicode Consortium — Mathematical character usage, variants, and notation support.
LaTeX Project DocumentationThe LaTeX Project — LaTeX syntax, authoring model, and official documentation links.
MathML CoreW3C — Semantic web mathematics elements and browser behavior.

Frequently asked questions

What does the Implies symbol mean?