How to write this symbol (vee with double line left)

Question

I want to write this symbol:

but cannot find anywhere how to do it. Detexify did'nt find it.

Edit: Thank you very much for your solutions but i forgot to write that i need this symbol in the size (and with the same behaviour) like "bigvee" I dont understand anything of the commands your solutions used, so i cannot change it myself, sorry.

Answer 1

Here's my proposal:

\documentclass{article}
\usepackage{amsmath}
\usepackage{pict2e,xfp}

\makeatletter
\newcommand{\dvee}{\mathbin{\mathpalette\d@vee\relax}}
\newcommand{\d@vee}[2]{%
  \begingroup
  \sbox\z@{$\m@th#1\vee$}%
  \setlength{\unitlength}{\ht\z@}%
  \kern0.1\wd\z@
  \begin{picture}(\fpeval{0.4\wd0/\unitlength},1)
  \roundcap\d@vee@thickness{#1}
  \Line(0,1.03)(\fpeval{0.4\wd0/\unitlength},0)
  \end{picture}%
  \kern-0.3\wd\z@\box\z@
  \endgroup
}
\newcommand{\d@vee@thickness}[1]{% see https://tex.stackexchange.com/a/477200/
  \linethickness{%
    1\fontdimen8
      \ifx#1\displaystyle\textfont\else
      \ifx#1\textstyle\textfont\else
      \ifx#1\scriptstyle\scriptfont\else
      \scriptscriptfont\fi\fi\fi 3
  }%
}
\makeatother

\begin{document}

$a \vee a \dvee a$\quad $\scriptstyle a \vee a \dvee a$

\fboxsep=0pt\fboxrule=0.1pt

\fbox{$\vee$}

\fbox{$\dvee$}

\end{document}

For the analog to \bigvee:

\documentclass{article}
\usepackage{amsmath}
\usepackage{pict2e,xfp}

\makeatletter
\newcommand{\bigdvee}{\mathop{\mathpalette\bigd@vee\relax}}
\newcommand{\bigd@vee}[2]{%
  \ifx#1\displaystyle
    \displaystylebigd@vee
  \else
    \begingroup
    \sbox\z@{$\m@th#1\bigvee$}%
    \setlength{\unitlength}{\dimexpr\ht\z@+\dp\z@}%
    \kern0.07\wd\z@
    \raisebox{-\dp\z@}{%
      \begin{picture}(\fpeval{0.45\wd0/\unitlength},1)
      \roundcap\bigd@vee@thickness{#1}%
      \Line(0.03,0.97)(\fpeval{0.45\wd0/\unitlength},0.03)
      \end{picture}%
    }%
    \kern-0.3\wd\z@\box\z@
    \endgroup
  \fi
}
\newcommand{\bigd@vee@thickness}[1]{% see https://tex.stackexchange.com/a/477200/
  \linethickness{%
    1.75\fontdimen8
      \ifx#1\textstyle\textfont\else
      \ifx#1\scriptstyle\scriptfont\else
      \scriptscriptfont\fi\fi 3
  }%
}
\def\displaystylebigd@vee{%
  \begingroup
  \sbox\z@{$\m@th\displaystyle\bigvee$}%
  \setlength{\unitlength}{0.825\dimexpr\ht\z@+\dp\z@}%
  \kern0.07\wd\z@
  \raisebox{-0.75\dp\z@}{%
    \begin{picture}(\fpeval{0.45\wd0/\unitlength},1)
    \roundcap\linethickness{2\fontdimen8\textfont3}
    \Line(0,1)(\fpeval{0.45\wd0/\unitlength},0)
    \end{picture}%
  }%
  \kern-0.3\wd\z@\box\z@
  \endgroup
}
\makeatother

\begin{document}

$\displaystyle \bigvee a + \bigdvee a$\quad
$\textstyle \bigvee a + \bigdvee a$\quad
$\scriptstyle a \bigvee a \bigdvee a$

\fboxsep=0pt\fboxrule=0.1pt

\fbox{$\bigvee$}

\fbox{$\bigdvee$}

\fbox{$\displaystyle\bigvee$}\fbox{$\displaystyle\bigdvee$}

\end{document}

Answer 2

I propose two solutions, based on the versions of leqslantin amssymb and mathabx (without loading the latter fonts):

\documentclass{article}
\usepackage{amssymb}
\usepackage{graphicx}
\newcommand{\dbvee}{\mathbin{\rotatebox[origin=c]{-90}{$ \geqslant $}}}

\DeclareFontFamily{U}{matha}{\hyphenchar\font45}
\DeclareFontShape{U}{matha}{m}{n}{ <-6> matha5 <6-7> matha6 <7-8>
matha7 <8-9> matha8 <9-10> matha9 <10-12> matha10 <12-> matha12 }{}
\DeclareSymbolFont{matha}{U}{matha}{m}{n}

\DeclareMathSymbol{\abxgeqslant}{\mathord}{matha}{"A5}
\newcommand{\abxdbvee}{\mathbin{\rotatebox[origin=c]{-90}{$ \abxgeqslant $}}}

\begin{document}

\[ A\dbvee B \qquad A\abxdbvee B\]%

\end{document} 

Edit:

To have the same symbol with \bigvee, you can add this to you preamble:

\usepackage{stackengine, mathtools}
\newcommand{\bigeqvee}{\stackMath\mathop{\stackinset{l}{-2pt}{c}{-0.5pt}{\scalebox{1.35}{$ \setminus $}}{\displaystyle\bigvee}}}

and type in the body of your document

\[ A = \bigeqvee_{\mathclap{i\in I}} A_i \]%

(of course this works only for display style. For a more general use, one would have to use \mathpalette, in order to adapt the code to textstyle, script style ans=d scriptscriptcstyle –) but will you need them?