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<b>let </b><font color="Maroon">X1</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">A1</font> be   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X1</font>;<br/><b>let </b><font color="Maroon">B1</font> be   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X1</font>;<br/>





<b>thus </b><a NAME="E1:39"/>
<font color="Maroon">A1</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">B1</font> <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <font color="Olive">x1</font> where <font color="Olive">x1</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X1</font> : ( <font color="Olive">x1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A1</font> &amp; not <font color="Olive">x1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B1</font> ) </span>}</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="39_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="E1:39_1"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A1</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">B1</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">x</font> = <font color="Maroon">a</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X1</font> ;<br/>
<a NAME="E3:39_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A1</font> &amp; not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B1</font> )
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<b>hence </b><a NAME="E4:39_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">x1</font> where <font color="Olive">x1</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X1</font> : ( <font color="Olive">x1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A1</font> &amp; not <font color="Olive">x1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B1</font> ) </span>}</span> 
 ;<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="E2:39"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">x1</font> where <font color="Olive">x1</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X1</font> : ( <font color="Olive">x1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A1</font> &amp; not <font color="Olive">x1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B1</font> ) </span>}</span> 
 ;<br/>

<a NAME="E3:39"/><b>then </b>
 ex <font color="Olive">x1</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X1</font> st <br/>( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Olive">x1</font> &amp; <font color="Olive">x1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A1</font> &amp; not <font color="Olive">x1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B1</font> )
 
;<br/>
<b>hence </b><a NAME="E4:39"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A1</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">B1</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>


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