How to type the letter-for-letter equivalence sign?

Question

I want to type the letter-for-letter equivalence symbol. Here's what it looks like:

This is found in Adian's "The Burnside Problem and Identities in Groups". Thanks in advance.

Answer 1

This seems to be a good substitute:

\documentclass{article}
\usepackage{amsmath,graphicx}

\newcommand{\lfleq}{%
  \mathrel{%
    \vphantom{=}%
    \ooalign{
      $=$\cr
      \hidewidth$\vcenter{\hbox{\scalebox{0.3}{\boldmath$\circ$}}}$\hidewidth\cr
    }%
  }%
}

\begin{document}

$A\lfleq B$

\end{document}

With a factor 0.4 you get

With stix2 you can use \eqcirc.

\documentclass{article}
\usepackage{amsmath}
\usepackage{stix2}

\begin{document}

$A\eqcirc B$

\end{document}

The same \eqcirc command is available to most math fonts with unicode-math.

\documentclass{article}
\usepackage{amsmath}
\usepackage{unicode-math}

\begin{document}

$A\eqcirc B$

\end{document}

Answer 2

Unicode math declares \eqcirc as U+02256, ≖. You can use it, but almost all fonts include it with the circle which touched the bars. If you want a little vertical space here (as in your image), you need to construct the relation symbol from two minus signs and the \circ between them.

\fontfam[lm]

\def\myeqcirc{\mathrel{\vcenter{\offinterlineskip
   \halign{\hfil$##$\hfil\cr-\cr \noalign{\kern-.48ex}
           \scriptstyle\circ\cr\noalign{\kern-.12ex}-\cr\noalign{\kern-.5ex}}}}}

$A\eqcirc B$

$A\myeqcirc B$
\bye

First result is from Unicode math font Latin Modern and the second one is composed from two minus signs.