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<div><span class="kw">theorem </span><a NAME="T67"><span class="comment"><font color="firebrick">:: FOMODEL0:67</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">Y</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">U</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="b3">x</font>, <font color="Olive" title="b4">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b2">U</font>  holds <br/> not <!--HUMANRECFAILED-->( ( <font color="Olive" title="b3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">Y</font> implies <font color="Olive" title="b4">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">Y</font> ) &amp; ( <font color="Olive" title="b4">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">Y</font> implies <font color="Olive" title="b3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">Y</font> ) &amp;  not <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="fomodel0.html#K10" title="FOMODEL0:func.10">chi</a> (<font color="Olive" title="b1">Y</font>,<font color="Olive" title="b2">U</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">x</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="fomodel0.html#K10" title="FOMODEL0:func.10">chi</a> (<font color="Olive" title="b1">Y</font>,<font color="Olive" title="b2">U</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">y</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a> ) <span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel0.html#E146"><span class="lab"><font color="Green" title="E91">Lm54</font></span></a></span>;<br/></div></div>
