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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E17">Th47</font></span>: <a NAME="T9"><span class="comment"><font color="firebrick">:: PROOFS_1:9</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">B</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">R</font> being   <a href="proofs_1.html#NM2" title="PROOFS_1:NM.2">Rule</a><br/>  for <font color="Olive" title="b3">S</font> being   <a href="proofs_1.html#NM3" title="PROOFS_1:NM.3">Formula-finset</a>  st (  for <font color="Olive" title="b4">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">S</font> holds <br/><font color="Olive" title="b1">B</font>,<font color="Olive" title="b2">R</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Olive" title="b4">a</font> ) holds <br/> ex <font color="Olive" title="b4">S1</font> being   <a href="proofs_1.html#NM3" title="PROOFS_1:NM.3">Formula-finset</a> st <br/>( <font color="Olive" title="b3">S</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b4">S1</font> &amp; <font color="Olive" title="b4">S1</font> is <font color="Olive" title="b1">B</font>,<font color="Olive" title="b2">R</font> <a href="proofs_1.html#V3" title="PROOFS_1:attr.3">-derivable</a>  )</div></div>
