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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="substut1.html#K16" target="_self">QC-Sub-WFF</a> ;<br/>

<a NAME="E1:31"/><i><font color="Green">E13</font></i>: 
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><a href="qc_lang1.html#K8">QC-WFF</a> ,<a href="substut1.html#K1" target="_self">vSUB</a> </span><a href="zfmisc_1.html#K2">:]</a></span> is <a href="substut1.html#V1" target="_self">QC-Sub-closed</a>
 
<b>by </b><i><a class="ref" href="substut1.html#D16" target="_self">Def16</a>, <a class="ref" href="substut1.html#T7" target="_self">Th7</a></i>;<br/>
<a NAME="E2:31"/>
 <a href="substut1.html#K16" target="_self">QC-Sub-WFF</a>  <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><a href="qc_lang1.html#K8">QC-WFF</a> ,<a href="substut1.html#K1" target="_self">vSUB</a> </span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="txt" href="substut1.html#E1:31"><i><font color="Green">E13</font></i></a>, <a class="ref" href="substut1.html#D17" target="_self">Def17</a></i>;<br/>
<a NAME="E3:31"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><a href="qc_lang1.html#K8">QC-WFF</a> ,<a href="substut1.html#K1" target="_self">vSUB</a> </span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:31"/><i><font color="Green">E14</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K8">QC-WFF</a>  &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="substut1.html#K1" target="_self">vSUB</a>  &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>2</sub></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="txt" href="substut1.html#E5:31"><i><font color="Green">E14</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> as    <a href="subset_1.html#M1">Element</a> of  <a href="substut1.html#K1" target="_self">vSUB</a>  <b>by </b><i><a class="txt" href="substut1.html#E5:31"><i><font color="Green">E14</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>4</sub></font>
;<br/>

<b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/>

<b>thus </b><a NAME="E8:31"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="domain_1.html#K1">]</a></span>
 <b>by </b><i><a class="txt" href="substut1.html#E5:31"><i><font color="Green">E14</font></i></a></i>;<br/>


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