How can I remove the qed symbols from all lemma proofs?

Question

the following code will only make the qed not appear in the second proof. However, it it possible to make the qed symbol never appear at the end of the proofs without having to specify it locally every time?

\documentclass{article}
\usepackage{amsthm}
\begin{document}
\begin{proof}
This has the QED symbol.
\end{proof}
\begin{proof}\renewcommand{\qedsymbol}{}
This hasn't.
\end{proof}
\begin{proof}
And this has it again.
\end{proof}
\end{document}

Answer 1

A simplistic solution would be adding

\renewcommand{\qedsymbol}{}

in the preamble, but this doesn't really work, as the following example shows:

\documentclass{article}
\usepackage{amsthm}

\renewcommand{\qedsymbol}{}

\begin{document}
\begin{proof}
A one liner
\end{proof}
\begin{proof}
This ends with a display
\[
0=0.
\]
\end{proof}
\begin{proof}
Another one liner.
\end{proof}
\end{document}

You should still have \qedhere in the display in order to get better spacing.

It's better to modify the definition of proof to remove the QED business.

\documentclass{article}
\usepackage{amsthm}

\makeatletter
\renewenvironment{proof}[1][\proofname]{\par
%  \pushQED{\qed}% <--- remove the QED business
  \normalfont \topsep6\p@\@plus6\p@\relax
  \trivlist
  \item[\hskip\labelsep
        \itshape
    #1\@addpunct{.}]\ignorespaces
}{%
%  \popQED% <--- remove the QED business
  \endtrivlist\@endpefalse
}
\renewcommand\qedhere{} % to ensure code portability
\makeatother

\begin{document}
\begin{proof}
A one liner
\end{proof}
\begin{proof}
This ends with a display
\[
0=0.
\]
\end{proof}
\begin{proof}
Another one liner.
\end{proof}
\end{document}

You can still have \qedhere, but it won't have any effect, so copying code where the command has been used won't give surprises.

Answer 2

If you don't want qed symbol in all proofs, use etoolbox and

\AtBeginEnvironment{proof}{\renewcommand{\qedsymbol}{}}{}{}

MWE:

\documentclass{article}
\usepackage{amsthm}
\usepackage{etoolbox}
\AtBeginEnvironment{proof}{\renewcommand{\qedsymbol}{}}{}{}
\begin{document}
\begin{proof}
This has the QED symbol.
\end{proof}
\begin{proof}
This hasn't.
\end{proof}
\begin{proof}
And this has it again.
\end{proof}
\end{document}

Or define a new myproof:

\documentclass{article}
\usepackage{amsthm}
\makeatletter
\newenvironment{myproof}[1][\proofname]{\par
  \normalfont \topsep6\p@\@plus6\p@\relax
  \trivlist
  \item[\hskip\labelsep
        \itshape
    #1\@addpunct{.}]\ignorespaces
}{%
  \endtrivlist\@endpefalse
}
\makeatother
\begin{document}
\begin{proof}
This has the QED symbol.
\end{proof}
\begin{myproof}
This hasn't.
\end{myproof}
\begin{proof}
And this has it again.
\end{proof}
\end{document}