<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T57"><span class="comment"><font color="firebrick">:: CQC_THE1:57</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">Al</font> being    <a href="qc_lang1.html#M1" title="QC_LANG1:mode.1">QC-alphabet</a> <br/>  for <font color="Olive" title="b2">X</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a> <font color="Olive" title="b1">Al</font></span>)</span><br/>  for <font color="Olive" title="b3">p</font>, <font color="Olive" title="b4">q</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a> <font color="Olive" title="b1">Al</font><br/>  for <font color="Olive" title="b5">x</font> being   <a href="qc_lang1.html#NM5" title="QC_LANG1:NM.5">bound_QC-variable</a> of <font color="Olive" title="b1">Al</font>  st <font color="Olive" title="b2">X</font> <a href="cqc_the1.html#R3" title="CQC_THE1:pred.3">|-</a> <font color="Olive" title="b3">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <font color="Olive" title="b4">q</font> &amp;  not <font color="Olive" title="b5">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="qc_lang1.html#K24" title="QC_LANG1:func.24">still_not-bound_in</a> <font color="Olive" title="b3">p</font> holds <br/><font color="Olive" title="b2">X</font> <a href="cqc_the1.html#R3" title="CQC_THE1:pred.3">|-</a> <font color="Olive" title="b3">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Olive" title="b5">x</font>,<font color="Olive" title="b4">q</font>)</span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the1.html#T13" target="_self" onmouseover="rs('cqc_the1/T13')" onmouseout="rh()">Th9</a></span>;<br/></div></div>
