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<b>let </b><font color="Maroon" title="c1">p</font>, <font color="Maroon" title="c2">q</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qc_lang1.html#K8" title="QC_LANG1:func.8">QC-WFF</a> ;<br/>



<a NAME="E1:62"/>
<font color="Maroon" title="c1">p</font> <a href="qc_lang2.html#K4" title="QC_LANG2:func.4">&lt;=&gt;</a> <font color="Maroon" title="c2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="qc_lang1.html#K13" title="QC_LANG1:func.13">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <font color="Maroon" title="c1">p</font></span>)</span>
 
<b>by </b><i><a class="ref" href="qc_lang2.html#D4" title="QC_LANG2:def.4">QC_LANG2:def 4</a></i>;<br/>
<b>hence </b> <a href="qc_lang3.html#K5" title="QC_LANG3:func.5">Free</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="qc_lang2.html#K4" title="QC_LANG2:func.4">&lt;=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="qc_lang3.html#K5" title="QC_LANG3:func.5">Free</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="qc_lang3.html#K5" title="QC_LANG3:func.5">Free</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="qc_lang3.html#T53" target="_self" title="QC_LANG3:th.53">Th53</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang3.html#K5" title="QC_LANG3:func.5">Free</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="qc_lang3.html#K5" title="QC_LANG3:func.5">Free</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="qc_lang3.html#K5" title="QC_LANG3:func.5">Free</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="qc_lang3.html#T72" target="_self" title="QC_LANG3:th.72">Th72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang3.html#K5" title="QC_LANG3:func.5">Free</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="qc_lang3.html#K5" title="QC_LANG3:func.5">Free</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang3.html#K5" title="QC_LANG3:func.5">Free</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="qc_lang3.html#K5" title="QC_LANG3:func.5">Free</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="qc_lang3.html#T72" target="_self" title="QC_LANG3:th.72">Th72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="qc_lang3.html#K5" title="QC_LANG3:func.5">Free</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="qc_lang3.html#K5" title="QC_LANG3:func.5">Free</a> <font color="Maroon" title="c2">q</font></span>)</span>

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