Implies in LaTeX (\implies)

Where it is used

Writes a long double arrow for logical implication, meaning the left statement implies the right.

\implies produces \Longrightarrow surrounded by extra thick spacing, which suits implications between whole statements, as in x > 2 \implies x^2 > 4. For implication between formulas inside a logic expression, many logicians prefer the shorter \Rightarrow or \to without the wide gap. Its converse is \impliedby. In proofs, avoid stacking several \implies in a row across a page; full sentences with "hence" often read better. In propositional logic notation, p \to q is more common than p \implies q.

Also listed under: Logic & Proofs

Minimal compilable example

Paste this into an empty .tex file and compile it with pdfLaTeX, XeLaTeX or LuaLaTeX.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
Implies: $\implies$

\[ x^2 = 4 \implies x = 2 \text{ or } x = -2 \]
\end{document}

Related symbols

• If and Only If\iff
• Greater Than or Equal\geq
• For All\forall
• Less Than or Equal\leq
• Exists\exists
• Not Equal\neq

Frequently asked questions

How do I write Implies in LaTeX?

Type \implies in math mode, for example $x^2 = 4 \implies x = 2 \text{ or } x = -2$. Load amsmath first with \usepackage{amsmath}.

Which package do I need for \implies?

\implies needs amsmath: add \usepackage{amsmath} to your preamble before the document starts.

Can I use \implies in text mode, or only in math mode?

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $\implies$ in running text. If you only need the glyph in text, paste the Unicode character ⟹ instead (with XeLaTeX or LuaLaTeX and a font that has it).