Left Arrow (Double) in LaTeX (\Leftarrow)

Where it is used

Draws a short double-shafted left arrow, read "is implied by" or marking the converse half of a proof.

In proofs of an equivalence, authors label the two directions (\Rightarrow) and (\Leftarrow), the latter proving the converse. Between formulas, A \Leftarrow B means B implies A. For a long, spaced version between full statements, \impliedby gives \Longleftarrow with extra space, mirroring \implies. Be careful not to confuse \Leftarrow with \leq in quick reading, since some readers misread the shape. Logic texts more often rearrange to use a right arrow, so reserve \Leftarrow for converse directions.

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}
Left Arrow (Double): $\Leftarrow$

\[ (\Leftarrow)\ \text{Suppose } n^2 \text{ is even. Then } n \text{ is even.} \]
\end{document}

Related symbols

• Right Arrow (Double)\Rightarrow
• Down Arrow\downarrow
• Up Arrow (Double)\Uparrow
• Long Right Arrow\longrightarrow
• Long Left Arrow (Double)\Longleftarrow
• Long Left Arrow\longleftarrow

Frequently asked questions

How do I write Left Arrow (Double) in LaTeX?

Type \Leftarrow in math mode, for example $(\Leftarrow)\ \text{Suppose } n^2 \text{ is even. Then } n \text{ is even.}$. It works in plain LaTeX without loading any package.

Which package do I need for \Leftarrow?

None. \Leftarrow is part of standard LaTeX, so it compiles with nothing in the preamble but the document class.

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

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $\Leftarrow$ 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).