Does the mirror image of the \models symbol exist in TeX?

Question

I've tried detexify, but it does not identity the symbol I saw in a textbook "A Mathematical Introduction to Logic", by Herbert Enderton.

The symbol is composed of two parts. The left looks like the \models and the right looks like its mirror image. It stands for tautological equivalence in the book.

I am looking for either the right hand symbol so I can create the symbol, or the combination symbol.

Answer 1

See The Comprehensive Symbol List. Examples:

MnSymbol

\documentclass{article}
\usepackage{MnSymbol}
\begin{document}
$\rightmodels\leftmodels$
\end{document}

mathabx

\documentclass{article}
\usepackage{mathabx}
\begin{document}
$\vDash\Dashv$
\end{document}

Symbol composition a la LaTeX

See Enrico Gregorio's comment. The definition of \models in LaTeX joins a vertical line | with the double horizontal line \RelBar.

\documentclass{article}

\DeclareRobustCommand*{\tautequiv}{%
  \mathrel{|}\joinrel\Relbar
  \Relbar\joinrel\mathrel{|}%
}

\begin{document}
\[ \tautequiv^{\tautequiv^{\tautequiv}} \]
\end{document}

\reflectbox

If the current math fonts do not provide the mirrored \models, then package graphics can help:

\documentclass{article}
\usepackage{graphicx}

\newcommand*{\tautequiv}{%
  \models\mirrormodels
}
\makeatletter
\newcommand*{\mirrormodels}{%
  \mathrel{%
    \mathpalette\reflectmathsymbol\models
  }%
}
\newcommand*{\reflectmathsymbol}[2]{%
  \reflectbox{$\m@th#1#2$}%
}
\makeatother

\begin{document}
\[ \tautequiv^{\tautequiv^{\tautequiv}} \]
\end{document}

Package accsupp

The /ActualText feature of the PDF format improves the copy&paste behaviour for PDF viewers the support this feature (e.g. Adobe Reader). Example:

\documentclass{article}

\usepackage{accsupp}

\DeclareRobustCommand*{\tautequiv}{%
  \BeginAccSupp{unicode,method=hex,ActualText=22A8 2AE4}%
    \mathrel{|}\joinrel\Relbar
    \Relbar\joinrel\mathrel{|}%
  \EndAccSupp{}%
}

\begin{document}
\[ \tautequiv^{\tautequiv^{\tautequiv}} \]
\end{document}