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

<b>assume </b><a NAME="E1:3"/><i><font color="Green">E48</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> holds <br/> ex <font color="Olive">K</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">K</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font> &amp; <font color="Olive">x</font> <a href="tarski.html#R1">c=</a>  <a href="tarski.html#K3">union</a> <font color="Olive">K</font> )
 ;<br/>

<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="E2:3"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">A</font>
 ;<br/>

<b>then consider </b><font color="Maroon">Z</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:3"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font>
 <b>and </b><br/><a NAME="E5:3"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">Z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon">K</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E7:3"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">K</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font>
 <b>and </b><br/><a NAME="E8:3"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">K</font>
 <b>by </b><i>, </i>;<br/>
<a NAME="E9:3"/>
 ex <font color="Olive">S</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Olive">S</font> &amp; <font color="Olive">S</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> )
 
<b>by </b><i>, , <a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>
<b>hence </b><a NAME="E10:3"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">B</font>
 <b>by </b><i>, <a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>


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