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<b>let </b><font color="Maroon">x</font> be   <a href="qc_lang1.html#NM3">bound_QC-variable</a>;<br/><b>let </b><font color="Maroon">y</font> be   <a href="qc_lang1.html#NM3">bound_QC-variable</a>;<br/><b>let </b><font color="Maroon">p</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a> ;<br/>





<b>set </b><font color="Maroon">q</font> =  <a href="qc_lang1.html#K14">All</a> <font color="Maroon">x</font>,<font color="Maroon">p</font>;<br/>
<a NAME="E1:56"/><i><font color="Green">E40</font></i>: 
 <a href="qc_lang1.html#K14">All</a> <font color="Maroon">x</font>,<font color="Maroon">p</font> is <a href="qc_lang1.html#V5">universal</a>
 
<b>by </b><i><a class="ref" href="qc_lang1.html#D20">QC_LANG1:def 20</a></i>;<br/>
<a NAME="E2:56"/><b>then </b>
(  <a href="qc_lang1.html#K21">the_scope_of</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K14">All</a> <font color="Maroon">x</font>,<font color="Maroon">p</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> &amp;  <a href="qc_lang1.html#K20">bound_in</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K14">All</a> <font color="Maroon">x</font>,<font color="Maroon">p</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> )
 
<b>by </b><i><a class="ref" href="qc_lang1.html#D26">QC_LANG1:def 26</a>, <a class="ref" href="qc_lang1.html#D27">QC_LANG1:def 27</a></i>;<br/>
<b>hence </b><a NAME="E3:56"/>
( <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y</font> implies <span class="p1">(<span class="default"><a href="qc_lang1.html#K14">All</a> <font color="Maroon">x</font>,<font color="Maroon">p</font></span>)</span> <a href="cqc_lang.html#K17" target="_self">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K14">All</a> <font color="Maroon">x</font>,<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="cqc_lang.html#K17" target="_self">.</a> <font color="Maroon">y</font></span>)</span> )
 <b>by </b><i>, </i>;<br/>


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