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<div><span class="kw">theorem </span><a NAME="T112"><span class="comment"><font color="firebrick">:: ZFMISC_1:112</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">N</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   ex <font color="Olive" title="b2">M</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  st <br/>( <font color="Olive" title="b1">N</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">M</font> &amp; (  for <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 <font color="Olive" title="b3">X</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">M</font> &amp; <font color="Olive" title="b4">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">X</font> holds <br/><font color="Olive" title="b4">Y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">M</font> ) &amp; (  for <font color="Olive" title="b3">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b3">X</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">M</font> holds <br/> <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Olive" title="b3">X</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">M</font> ) &amp; (  for <font color="Olive" title="b3">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   holds <br/>(  not <font color="Olive" title="b3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">M</font> or <font color="Olive" title="b3">X</font>,<font color="Olive" title="b2">M</font> <a href="tarski.html#R3" title="TARSKI:pred.3">are_equipotent</a>  or <font color="Olive" title="b3">X</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">M</font> ) ) )</div></div>
