Vertical space between “Proof” and start of proof

Question

How can you add vertical space between the word "Proof" and the actual start of the proof? This question shows how to start the proof on a new line, but I can't add space properly.

Answer 1

You can use the optional argument for \\ (I used 3ex in my example, but change to the desired value):

\documentclass{article}
\usepackage{amsthm}
\usepackage{lipsum}% just to generate text for the example

\makeatletter
\renewenvironment{proof}[1][\proofname]{\par
  \pushQED{\qed}%
  \normalfont \topsep6\p@\@plus6\p@\relax
  \trivlist
  \item[\hskip\labelsep
        \itshape
    #1\@addpunct{.}]\mbox{}\\*[3ex]
}{%
  \popQED\endtrivlist\@endpefalse
}
\makeatother

\begin{document}

\begin{proof}
\lipsum*[1]
\end{proof}

\end{document}