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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E4">Th4</font></span>: <a NAME="T4"><span class="comment"><font color="firebrick">:: FRAENKEL:4</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">B</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> <br/>  for <font color="Olive" title="b2">A</font>, <font color="Olive" title="b3">X</font>, <font color="Olive" title="b4">Y</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st  <a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> (<font color="Olive" title="b3">X</font>,<font color="Olive" title="b4">Y</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Olive" title="b3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">A</font> &amp; <font color="Olive" title="b4">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">B</font> holds <br/> for <font color="Olive" title="b5">f</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> (<font color="Olive" title="b3">X</font>,<font color="Olive" title="b4">Y</font>)  ex <font color="Olive" title="b6">phi</font> being    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Olive" title="b2">A</font>,<font color="Olive" title="b1">B</font>) st <font color="Olive" title="b6">phi</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b3">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">f</font></div></div>
