The command you need is already there:
\impliedby (if you're using
\implies it means that you're loading
The story is quite intricated. Let's try doing a resumé.
Plain TeX defines
\;\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":
and it was supplemented by similar commands
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
but also this can be risky, since it uses the internal macro
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