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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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_lang2.html#K5" title="QC_LANG2:func.5">Ex</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/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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_lang2.html#K5" title="QC_LANG2:func.5">Ex</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/>



<b>assume </b><a NAME="E1:35"/>
 <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> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="qc_lang1.html#D30" title="QC_LANG1:def.30">QC_LANG1:def 30</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="qc_lang2.html#K5" title="QC_LANG2:func.5">Ex</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="E2:35"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T2" title="XBOOLE_1:th.2">XBOOLE_1:2</a></i>;<br/>
<b>hence </b><a NAME="E3:35"/>
 <a href="qc_lang2.html#K5" title="QC_LANG2:func.5">Ex</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>
 <b>by </b><i><a class="ref" href="qc_lang3.html#T32" target="_self" title="QC_LANG3:th.32">Th32</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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