[Tex/LaTex] How to put therefore and implies symbols

Question

\documentclass{article}
\usepackage{graphicx}

\begin{document}
\vspace{\baselineskip}\noindent
\textbf{THEOREM :} If an operator has both Left Identity and Right Identity then it is \emph{UNIQUE}.
\vspace{\baselineskip}\noindent
\textbf{PROOF :} Let e_{l} is left identity 
                         therefore e_{l} * e_{r} 
                             this implies e_{r}
\end{document}

Answer 1

As stated in the comments, you get the symbols in mathmode simply by writing them down. Packages like amsmath and amssymb support you.

\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\newtheorem{theorem}{THEOREM}
\newtheorem{proof}{PROOF}
\begin{document}
\begin{theorem}
If an operator has both Left Identity and
Right Identity then it is \emph{UNIQUE}.
\end{theorem}
\begin{proof}
Let $e_{l}$ is left identity 
$\therefore e_{l} * e_{r} \implies e_{r}$
\end{proof}
\end{document}