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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E13">Th30</font></span>: <a NAME="T30"><span class="comment"><font color="firebrick">:: QC_LANG2:30</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font> being    <a href="qc_lang1.html#M1" title="QC_LANG1:mode.1">QC-alphabet</a> <br/>  for <font color="Olive" title="b2">F</font>, <font color="Olive" title="b3">G</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qc_lang1.html#K9" title="QC_LANG1:func.9">QC-WFF</a> <font color="Olive" title="b1">A</font> holds <br/> (  <a href="qc_lang2.html#K12" title="QC_LANG2:func.12">the_antecedent_of</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">F</font> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <font color="Olive" title="b3">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">F</font> &amp;  <a href="qc_lang2.html#NK13" title="QC_LANG2:NK.13">the_consequent_of</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">F</font> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <font color="Olive" title="b3">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">G</font> &amp;  <a href="qc_lang1.html#K18" title="QC_LANG1:func.18">the_argument_of</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">F</font> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <font color="Olive" title="b3">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">F</font> <a href="qc_lang1.html#K14" title="QC_LANG1:func.14">'&amp;'</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K13" title="QC_LANG1:func.13">'not'</a> <font color="Olive" title="b3">G</font></span>)</span> )</div></div>
