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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E24">Th10</font></span>: <a NAME="T10"><span class="comment"><font color="firebrick">:: ZF_FUND1:10</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font> being   <a href="classes2.html#NM1" title="CLASSES2:NM.1">Universe</a><br/>  for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">V</font><br/>  for <font color="Olive" title="b4">X</font> being   <a href="zf_refle.html#NM1" title="ZF_REFLE:NM.1">Subclass</a> of <font color="Olive" title="b1">V</font><br/>  for <font color="Olive" title="b5">fs</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a>  st <font color="Olive" title="b4">X</font> is  <a href="zf_fund1.html#V8" title="ZF_FUND1:attr.8">closed_wrt_A1-A7</a>  &amp; <font color="Olive" title="b2">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Olive" title="b5">fs</font>,<a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a>) &amp; <font color="Olive" title="b3">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">X</font> holds <br/><span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b2">a</font> <a href="zf_fund1.html#K1" title="ZF_FUND1:func.1">(#)</a> <font color="Olive" title="b6">x</font></span>)</span> where <font color="Olive" title="b6">x</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">V</font> : <font color="Olive" title="b6">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">b</font> </span> } </span>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">X</font></div></div>
