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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#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> ;<br/>



<b>assume </b><a NAME="E1:59"/><i><font color="Green" title="E45">A1</font></i>: 
(  <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="substut1.html#K9" title="SUBSTUT1:func.9">Bound_Vars</a> <font color="Maroon" title="c1">p</font> &amp;  <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c2">q</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="substut1.html#K9" title="SUBSTUT1:func.9">Bound_Vars</a> <font color="Maroon" title="c2">q</font> )
 ;<br/>

<a NAME="E2:59"/>
<font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font> is <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a>
 
<b>by </b><i><a class="ref" href="qc_lang1.html#D19" title="QC_LANG1:def.19">QC_LANG1:def 19</a></i>;<br/>
<a NAME="E3:59"/><b>then </b>
 <a href="substut1.html#K9" title="SUBSTUT1:func.9">Bound_Vars</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="substut1.html#K9" title="SUBSTUT1:func.9">Bound_Vars</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K18" title="QC_LANG1:func.18">the_left_argument_of</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="substut1.html#K9" title="SUBSTUT1:func.9">Bound_Vars</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K19" title="QC_LANG1:func.19">the_right_argument_of</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="substut1.html#T5" title="SUBSTUT1:th.5">SUBSTUT1:5</a></i>;<br/>
<a NAME="E4:59"/><b>then </b>
 <a href="substut1.html#K9" title="SUBSTUT1:func.9">Bound_Vars</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="substut1.html#K9" title="SUBSTUT1:func.9">Bound_Vars</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="substut1.html#K9" title="SUBSTUT1:func.9">Bound_Vars</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K19" title="QC_LANG1:func.19">the_right_argument_of</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="qc_lang2.html#T5" title="QC_LANG2:th.5">QC_LANG2:5</a></i>;<br/>
<a NAME="E5:59"/><b>then </b><i><font color="Green" title="E46">A2</font></i>: 
 <a href="substut1.html#K9" title="SUBSTUT1:func.9">Bound_Vars</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="substut1.html#K9" title="SUBSTUT1:func.9">Bound_Vars</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="substut1.html#K9" title="SUBSTUT1:func.9">Bound_Vars</a> <font color="Maroon" title="c2">q</font></span>)</span>
 
<b>by </b><i><a class="ref" href="qc_lang2.html#T5" title="QC_LANG2:th.5">QC_LANG2:5</a></i>;<br/>
<a NAME="E6:59"/>
 <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</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_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c2">q</font></span>)</span>
 
<b>by </b><i><a class="ref" href="qc_lang3.html#T14" title="QC_LANG3:th.14">QC_LANG3:14</a></i>;<br/>
<b>hence </b><a NAME="E7:59"/>
 <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="substut1.html#K9" title="SUBSTUT1:func.9">Bound_Vars</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span>
 <b>by </b><i><a class="txt" href="sublemma.html#E1:59"><i><font color="Green" title="E45">A1</font></i></a>, <a class="txt" href="sublemma.html#E5:59"><i><font color="Green" title="E46">A2</font></i></a>, <a class="ref" href="xboole_1.html#T13" title="XBOOLE_1:th.13">XBOOLE_1:13</a></i>;<br/>


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