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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>assume </b><a NAME="E1:24_1"/><i><font color="Green">E20</font></i>: 
for <font color="Olive">x1</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X1</font>  st <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">x1</font>] holds <br/><font color="Maroon">P<sub>2</sub></font>[<font color="Olive">x1</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="E2:24_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="Maroon">P<sub>1</sub></font>[<font color="Olive">x1</font>] </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">x1</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X1</font><b> such that </b><br/><a NAME="E4:24_1"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font>
 <b>and </b><br/><a NAME="E5:24_1"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">x1</font>]
 ;<br/>
<a NAME="E6:24_1"/>
<font color="Maroon">P<sub>2</sub></font>[<font color="Maroon">x1</font>]
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E7:24_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">z1</font> where <font color="Olive">z1</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X1</font> : <font color="Maroon">P<sub>2</sub></font>[<font color="Olive">z1</font>] </span>}</span> 
 <b>by </b><i/>;<br/>


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