# Is there a left-handed equivalent of \implies?

I use the \implies and \iff command for right-handed implication and if and only if (so A=>B and A<=>B).

What’s a similar command for left-handed implication (i.e., A<=B)? I couldn’t find anything in Google or the documentation.

• There's also \Leftarrow – kan Oct 31 '12 at 12:33
• Everyone always overlooks the obvious solution to a "missing" character macro: \newcommand\follows{\Longleftarrow}. – Ryan Reich Oct 31 '12 at 12:43
• With \usepackage{amsmath} you have \impliedby – egreg Oct 31 '12 at 12:49
• @cmhughes Not really. The commands \implies and \iff are provided by amsmath, but somehow slipped away from the documentation. The command \impliedby is there also. The three behave correctly with respect to dots, while the \Long...arrow commands don't. The symbol.pdf file doesn't list them. – egreg Oct 31 '12 at 16:29

The command you need is already there: \impliedby (if you're using \implies it means that you're loading amsmath).

The story is quite intricated. Let's try doing a resumé.

Plain TeX defines \iff as \;\Longleftrightarrow\;, that is, a relation symbol with extended spaces on its left and right.

In AMS-TeX the command was redefined so that it was "dots-aware":

\def\iff{\DOTSB\;\Longleftrightarrow\;}


and it was supplemented by similar commands

\def\implies{\DOTSB\;\Longrightarrow\;}
\def\impliedby{\DOTSB\;\Longleftarrow\;}


The three commands were transplanted in amstex.sty (the first porting of AMS-TeX to LaTeX) and found their way also in the "definitive" package amsmath.sty, but not in its documentation.

Since they are undocumented, they aren't really listed in the Comprehensive List of LaTeX Symbols (there are "see \Longrightarrow" and similar references).

A problem can arise from the fact the commands are not documented: they may disappear in new releases of amsmath. A solution for your documents is to say

\usepackage{amsmath}
\providecommand\iff{\DOTSB\;\Longleftrightarrow\;}
\providecommand\implies{\DOTSB\;\Longrightarrow\;}
\providecommand\impliedby{\DOTSB\;\Longleftarrow\;}


but also this can be risky, since it uses the internal macro \DOTSB.

Since they are useful (although I usually stay away from them, preferring words) it would be a welcome addition that they find their way in the documentation of amsmath.

• What does it mean for a symbol to be "dots-aware"? – Andrew Uzzell Nov 1 '12 at 11:38
• @AndrewUzzell When you say $a+\dots+z$ you get centered dots, when you say $a,\dots,z$ the dots are low. Similarly, you automatically get centered dots with $a\iff\dots\iff z$ because of \DOTSB – egreg Nov 1 '12 at 11:40
• I see. That's a neat feature. – Andrew Uzzell Nov 1 '12 at 11:41
• Is there a more complete list of such undocumented symbol commands? It seems that \to might belong here as well. – Ari Brodsky Jul 4 '13 at 5:11
• @AriBrodsky \to has been equivalent to \rightarrow since the beginning of (TeX) time. I've always taken for granted it's in the LaTeX manual, but to my surprise it isn't there. – egreg Jul 4 '13 at 8:37