<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T5"><span class="comment"><font color="firebrick">:: ZFMODEL1:5</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">E</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">E</font> is  <a href="ordinal1.html#V1" title="ORDINAL1:attr.1">epsilon-transitive</a>  holds <br/>( <font color="Olive" title="b1">E</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a>  <a href="zf_model.html#K8" title="ZF_MODEL:func.8">the_axiom_of_unions</a>  iff  for <font color="Olive" title="b2">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b2">X</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">E</font> holds <br/> <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Olive" title="b2">X</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">E</font> )</div></div>
