\documentclass{IEEEtran}
\usepackage{amsmath}
\usepackage{amsthm}
\newtheorem{theorem}{Theorem}
\title{IEEE Trans}
\begin{document}

\IEEEtitleabstractindextext{%
\begin{abstract}
Uncertainty from blah, blah
\end{abstract}
\begin{IEEEkeywords}
Stuff, More Stuff
\end{IEEEkeywords}
}
\section{A Theorem}
\begin{theorem}\label{th1}
Whenever this, then that.
\end{theorem}
\begin{IEEEproof}[Proof of Theorem~\ref{th1}]
Because I say so.

This completes the proof.
\end{IEEEproof}

\section{IEEE style eqnarray}

Normal numbering.
\begin{IEEEeqnarray}{rCl}
N &=& \theequation\\
N &=& \theequation
\end{IEEEeqnarray}

No numbering.
\begin{IEEEeqnarray*}{rCl}
N &=& \theequation\\
N &=& \theequation
\end{IEEEeqnarray*}

Only number first
\begin{IEEEeqnarray*}{rCl}
\IEEEyesnumber
N &=& \theequation\\
N &=& \theequation
\end{IEEEeqnarray*}

Normal numbering, done differently
\begin{IEEEeqnarray*}{rCl}
\IEEEyesnumber*
N &=& \theequation\\
N &=& \theequation
\end{IEEEeqnarray*}

Only number last.
\begin{IEEEeqnarray}{rCl}
\IEEEnonumber
N &=& \theequation\\
N &=& \theequation
\end{IEEEeqnarray}
Same done differently
\begin{IEEEeqnarray*}{rCl}
N &=& \theequation\\
\IEEEyesnumber
N &=& \theequation
\end{IEEEeqnarray*}

Number all
\begin{IEEEeqnarray}{rCl}
\IEEEyesnumber
N &=& \theequation\\
N &=& \theequation
\end{IEEEeqnarray}

Sub-number first
\begin{IEEEeqnarray}{rCl}
\IEEEyesnumber\IEEEyessubnumber
N &=& \theequation\\
N &=& \theequation
\end{IEEEeqnarray}

Sub-number persistently
\begin{IEEEeqnarray}{rCl}
\IEEEyesnumber\IEEEyessubnumber*
N &=& \theequation\\
N &=& \theequation
\end{IEEEeqnarray}

Resume normal numbering
\begin{IEEEeqnarray}{rCl}
N &=& \theequation\\
N &=& \theequation
\end{IEEEeqnarray}

And boxed?
\begin{IEEEeqnarraybox}{rCl}
N &=& \theequation\\
N &=& \theequation
\end{IEEEeqnarraybox}

Mixed case, single column
\begin{IEEEeqnarray}{c}
x_1\IEEEyesnumber\IEEEyessubnumber*\\
x_2\\
x_3\IEEEyesnumber\IEEEyessubnumber\label{eqn:expl}\\
x_4\\
x_5\IEEEyesnumber*\\
x_6
\end{IEEEeqnarray}

\begin{IEEEbiography}[{Picture of Me}]{ME}ME is a really great guy.
\end{IEEEbiography}

\end{document}
