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<div><span class="kw">theorem </span><a NAME="T47"><span class="comment"><font color="firebrick">:: VALUAT_1:47</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">A</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="qc_lang1.html#NM5" title="QC_LANG1:NM.5">bound_QC-variable</a> of <font color="Olive" title="b1">Al</font><br/>  for <font color="Olive" title="b5">p</font>, <font color="Olive" title="b6">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="b7">J</font> being    <a href="valuat_1.html#M1" title="VALUAT_1:mode.1">interpretation</a> of <font color="Olive" title="b1">Al</font>,<font color="Olive" title="b2">A</font><br/>  for <font color="Olive" title="b8">s</font> being   <a href="qc_lang1.html#NM10" title="QC_LANG1:NM.10">QC-formula</a> of <font color="Olive" title="b1">Al</font>  st <font color="Olive" title="b5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b8">s</font> <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">.</a> <font color="Olive" title="b3">x</font> &amp; <font color="Olive" title="b6">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b8">s</font> <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">.</a> <font color="Olive" title="b4">y</font> &amp;  not <font color="Olive" title="b3">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="b8">s</font> &amp; <font color="Olive" title="b7">J</font> <a href="valuat_1.html#R2" title="VALUAT_1:pred.2">|=</a> <font color="Olive" title="b5">p</font> holds <br/><font color="Olive" title="b7">J</font> <a href="valuat_1.html#R2" title="VALUAT_1:pred.2">|=</a> <font color="Olive" title="b6">q</font></div></div>
