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<b>thus </b><a NAME="E1:85"/>
 <a href="qc_lang2.html#K15" target="_self">Subformulae</a> <a href="qc_lang2.html#K1" target="_self">FALSUM</a>  <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><a href="qc_lang1.html#K11">VERUM</a> ,<a href="qc_lang2.html#K1" target="_self">FALSUM</a> </span><a href="tarski.html#K2">}</a></span>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="85_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:85_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="qc_lang2.html#K15" target="_self">Subformulae</a> <a href="qc_lang2.html#K1" target="_self">FALSUM</a> 
 ;<br/>

<a NAME="E2:85_1"/><b>then </b>
 ex <font color="Olive">F</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a>  st <br/>( <font color="Olive">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Olive">F</font> <a href="qc_lang2.html#R2" target="_self">is_subformula_of</a>  <a href="qc_lang2.html#K1" target="_self">FALSUM</a>  )
 
<b>by </b><i/>;<br/>
<a NAME="E3:85_1"/><b>then </b>
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="qc_lang2.html#K1" target="_self">FALSUM</a>  or <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K11">VERUM</a>  )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:85_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><a href="qc_lang1.html#K11">VERUM</a> ,<a href="qc_lang2.html#K1" target="_self">FALSUM</a> </span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:85"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><a href="qc_lang1.html#K11">VERUM</a> ,<a href="qc_lang2.html#K1" target="_self">FALSUM</a> </span><a href="tarski.html#K2">}</a></span>
 ;<br/>

<a NAME="E3:85"/><b>then </b><i><font color="Green">E29</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K11">VERUM</a>  or <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="qc_lang2.html#K1" target="_self">FALSUM</a>  )
 
<b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon">a</font> = <font color="Maroon">a</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a>  <b>by </b><i>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<a NAME="E5:85"/>
<font color="Maroon">a</font> <a href="qc_lang2.html#R2" target="_self">is_subformula_of</a>  <a href="qc_lang2.html#K1" target="_self">FALSUM</a> 
 
<b>by </b><i><a class="ref" href="qc_lang2.html#T45" target="_self">Th45</a>, </i>;<br/>
<b>hence </b><a NAME="E6:85"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="qc_lang2.html#K15" target="_self">Subformulae</a> <a href="qc_lang2.html#K1" target="_self">FALSUM</a> 
 <b>by </b><i/>;<br/>


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