# Animating tabular rows in Beamer without showing the table border

I have a tabular environment with three rows, and I would like to show only the first row on my first slide, then show the next row and finally the third row. I have a solution that almost works but it shows borders around rows 2 and 3 when they are not visible, which I don't like. Is there a way to get rid of these empty borders?

Here is my code:

\documentclass{beamer}

\mode<presentation>
{
\usetheme{default}
\useinnertheme{rounded}
\usecolortheme{default}
}

\begin{document}

\begin{frame}{Test Frame}

{\footnotesize
\begin{tabular}{|p{4.0cm}|p{2.9cm}|p{2.950cm}|}
\hline
\textbf{Constraint Explanation} & \textbf{Assumptions} & \textbf{Notation} \\ \hline
Each gate covered by only one module & Suppose gate $g$ is covered by modules $i$, $j$ and $k$ & $Var(g,i) + Var(g,j) + Var(g,k) \leq 1$ \\ \hline
\onslide<2-> {Selecting a slice in the module implies selecting the common parts of the module & Module $i$ has $n$ slices & forall $1 \leq k \leq n: x_{i_0} - x_{i_k} \geq 0$} \\ \hline
\onslide<3->{Each sliceable module must select either at least $M$ slices or no slices at all & Module $i$ has $n$ slices & \big( $\sum_{k=1}^n x_{i_k} \big) ~-~ M\cdot x_{i_{0}} \geq 0$} \\ \hline
\end{tabular}
}
\end{frame}

\end{document}


The image I get is the following.

What I would like exactly the same as the above but without the borders around the second and third rows.

\documentclass{beamer}

\mode<presentation>
{
\usetheme{default}
\useinnertheme{rounded}
\usecolortheme{default}
}

\begin{document}
\makeatletter
\let\slideno\beamer@slideinframe
\makeatother

\begin{frame}[t]{Test Frame}
\onslide<2> {}
\onslide<3-> {}
{\footnotesize
\begin{tabular}{|p{4.0cm}|p{2.9cm}|p{2.950cm}|}
\hline
\textbf{Constraint Explanation} & \textbf{Assumptions} & \textbf{Notation} \\ \hline
Each gate covered by only one module & Suppose gate $g$ is covered by modules $i$, $j$ and $k$ & $Var(g,i) + Var(g,j) + Var(g,k) \leq 1$ \\ \hline
\ifnum\slideno>1
Selecting a slice in the module implies selecting the common parts of the module & Module $i$ has $n$ slices & forall $1 \leq k \leq n: x_{i_0} - x_{i_k} \geq 0$\\ \hline
\ifnum\slideno>2
Each sliceable module must select either at least $M$ slices or no slices at all & Module $i$ has $n$ slices & \big( $\sum_{k=1}^n x_{i_k} \big) ~-~ M\cdot x_{i_{0}} \geq 0$\\ \hline
\fi\fi
\end{tabular}
}
\end{frame}

\end{document}