Select rows that satisfy a certain group condition in psql
<p>Given the following table:  </p>

<pre><code> id  |  value 
  ---+---------
  1  |    1 
  1  |    0
  1  |    3
  2  |    1
  2  |    3
  2  |    5
  3  |    2 
  3  |    1
  3  |    0
  3  |    1
</code></pre>

<p>I want the following table: </p>

<pre><code> id  |  value 
  ---+---------
  1  |    1 
  1  |    0
  1  |    3
  3  |    2 
  3  |    1
  3  |    0
  3  |    1
</code></pre>

<p>The table contains <code>ids</code> that have a minimum <code>value</code> of 0.
I have tried using <code>exist</code> and <code>having</code> but to no success.</p>