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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ] <b>means </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<sub>1</sub></font> &amp; <font color="Olive">F</font> <a href="qc_lang2.html#R2" target="_self">is_subformula_of</a> <font color="Maroon">H</font> );<br/>
<b>consider </b><font color="Maroon">X</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E2:79_1_1"/><i><font color="Green">E28</font></i>: 
for <font color="Olive">a</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> iff ( <font color="Olive">a</font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K8">QC-WFF</a>  &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">a</font>] ) )
 <b>from </b><i><a class="ref" href="xboole_0.html#S1">XBOOLE_0:sch 1</a>();<br/></i>
<b>take </b>
<font color="Maroon">X</font>
;<br/>

<b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>thus </b><a NAME="E3:79_1_1"/>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> implies  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> <font color="Maroon">H</font> ) )
 <b>by </b><i/>;<br/>

<b>given </b><font color="Maroon">F</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a> <b> such that </b><a NAME="E4:79_1_1"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">F</font> <a href="qc_lang2.html#R2" target="_self">is_subformula_of</a> <font color="Maroon">H</font> )
 ;<br/>

<b>thus </b><a NAME="E5:79_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 <b>by </b><i>, <a class="ref" href="qc_lang2.html#D11" target="_self">Def11</a></i>;<br/>


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