The actual style that you want to update is the definition
style (since you specify it), like so:
\documentclass{amsart}
\begin{document}
\makeatletter
\def\th@definition{
\thm@headfont{\itshape} % Heading font is italic
\thm@notefont{} % Note is same as heading
\itshape% Regular text is also italic
}
\makeatother
\theoremstyle{definition}
\newtheorem*{prop}{Proposition}
\begin{prop}[Optional Title]
Content.
\end{prop}
\end{document}
Edit:
Note that the same result can be made with the article
class by loading amsthm
... nearly all of the same code is used in both cases, so the same trick will apply in either setting. From the documentation:
Three document class files and one package file (amsthm.sty) are produced from
this source. Most of the code of the amsthm
package is used in all four derived
files.
For example:
\documentclass{article}
\usepackage{amsthm}
\begin{document}
\makeatletter
\def\th@definition{
\thm@headfont{\itshape} % Heading font is italic
\thm@notefont{} % Note is same as heading
\itshape% Regular text is also italic
}
\makeatother
\theoremstyle{definition}
\newtheorem*{prop}{Proposition}
\begin{prop}[Optional Title]
Content.
\end{prop}
\end{document}
ntheorem
oramsthm
?