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<div><span class="kw">theorem </span><a NAME="T45"><span class="comment"><font color="firebrick">:: SUBSET_1:45</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">D</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">A</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Olive" title="b1">D</font>  st  not <font color="Olive" title="b2">A</font> is  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a>  holds <br/> ex <font color="Olive" title="b3">d1</font>, <font color="Olive" title="b4">d2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">D</font> st <br/>( <font color="Olive" title="b3">d1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">A</font> &amp; <font color="Olive" title="b4">d2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">A</font> &amp; <font color="Olive" title="b3">d1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">d2</font> )</div></div>
