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<span class="kw">let </span><font color="Maroon" title="c1">x</font> be   <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">p</font> being   <a href="qc_lang1.html#NM8" title="QC_LANG1:NM.8">QC-formula</a>  st <font color="Olive" title="b1">p</font> is  <a href="qc_lang1.html#V6" title="QC_LANG1:attr.6">closed</a>  holds <br/> <a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> (<font color="Maroon" title="c1">x</font>,<font color="Olive" title="b1">p</font>) is  <a href="qc_lang1.html#V6" title="QC_LANG1:attr.6">closed</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font> be   <a href="qc_lang1.html#NM8" title="QC_LANG1:NM.8">QC-formula</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">p</font> is  <a href="qc_lang1.html#V6" title="QC_LANG1:attr.6">closed</a>  implies  <a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">p</font>) is  <a href="qc_lang1.html#V6" title="QC_LANG1:attr.6">closed</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:30"/>
 <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="qc_lang1.html#D29" title="QC_LANG1:def.29">QC_LANG1:def 29</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">p</font>) is  <a href="qc_lang1.html#V6" title="QC_LANG1:attr.6">closed</a> </span><br/>

<a NAME="E2:30"/><span class="kw">then </span>
 <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c2">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T2" title="XBOOLE_1:th.2">XBOOLE_1:2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:30"/>
 <a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">p</font>) is  <a href="qc_lang1.html#V6" title="QC_LANG1:attr.6">closed</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang3.html#T23" target="_self" title="QC_LANG3:th.23">Th27</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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