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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:30_1_2"/><i><font color="Green">E11</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> is <a href="substut1.html#V1" target="_self">QC-Sub-closed</a> &amp; ( for <font color="Olive">b<sub>1</sub></font> being non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> is <a href="substut1.html#V1" target="_self">QC-Sub-closed</a> holds <br/><font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> ) )
 <b>and </b><br/><a NAME="E2:30_1_2"/><i><font color="Green">E12</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> is <a href="substut1.html#V1" target="_self">QC-Sub-closed</a> &amp; ( for <font color="Olive">b<sub>1</sub></font> being non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> is <a href="substut1.html#V1" target="_self">QC-Sub-closed</a> holds <br/><font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> ) )
 ;<br/>

<a NAME="E3:30_1_2"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="substut1.html#E1:30_1_2"><i><font color="Green">E11</font></i></a>, <a class="txt" href="substut1.html#E2:30_1_2"><i><font color="Green">E12</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:30_1_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


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