\documentclass[journal]{IEEEtran}
\usepackage{amssymb, amsmath, amsthm, amsfonts}
\usepackage{showframe} % just to show the margins
\newtheorem{thm}{Theorem}
%% define a \killproofname command that works with both
%% IEEEtran.cls version 1.7a or version 1.8
\makeatletter
\@ifclasslater{IEEEtran}{2012/12/26}
{\newcommand{\killproofname}{\unskip\nopunct}}
{\newcommand{\killproofname}[1]{\unskip\aftergroup\ignorespaces\ignorespaces}}
\makeatother
\begin{document}
\begin{proof}[\killproofname]
We will use induction to prove this theorem.