How to stop numbering the word proof in my document and to put the square at the end of my proofs?

Question

Here is my document from the beginning:

\documentclass{book}
\usepackage[margin=1in]{geometry}
\usepackage{datetime2}
\usepackage{lipsum}

\DTMsetstyle{mmddyy}
\DTMsetup{datesep=/}

\usepackage{fancyhdr}
\fancyhead[L]{\sffamily Jack}
\fancyhead[C]{\bfseries RAT : Homework 4}
\fancyhead[R]{\today}
\pagestyle{fancy}

\usepackage{tcolorbox}
\tcbuselibrary{theorems}
\newtcbtheorem[auto counter, number within=section]{problem}{Problem}{
    fonttitle=\bfseries,
    colframe=black,
    coltitle=black,
    colback=black!10,
    colbacktitle=black!10,
    boxrule=.4pt,
    attach title to upper=\newline,
    sharp corners,
    top=1mm, bottom=1mm,
    left=2mm, right=2mm,
}{}
\newtheorem{pro}{\emph{Proof}}
\begin{document}

%\begin{center}
   % \sffamily
    %Title
%\end{center}

\setcounter{chapter}{7}
\setcounter{section}{2}
\begin{problem}[phantom=\setcounter{\tcbcounter}{13}]{}{}
\lipsum[1]
\end{problem}

\begin{pro}


\end{pro}

\end{document}

But I am wondering how can I stop numbering the word proof in my document and to put the square at the end of my proofs?

Any help will be greatly appreciated!

EDIT:

Here is how my document looks like now:

Answer 1

You may use add these two lines before this line \newtheorem{pro}{\emph{Proof}} in your code to serve your purpose.

\usepackage{ntheorem}
\theoremstyle{nonumberplain}

EDIT:

Another solution can be proposed:

\usepackage{amssymb}
\usepackage[thmmarks]{ntheorem}
\theoremheaderfont{\bfseries}
\theorembodyfont{\normalfont}
\theoremsymbol{$\blacksquare$} 
\newtheorem*{pro}{\emph{Proof}}

Answer 2

If you load the amsthm package it will give you a proof environment that will do what you want (although there are some special cases, such as when your proof ends with a displayed equation or a list where you will need to use \qedhere to produce the proof box at the correct location.