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<b>let </b><font color="Maroon">X1</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">X2</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">f</font> be   <a href="funct_1.html#NM1">Function</a>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:103"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">f</font> <a href="relat_1.html#K9">.:</a> <font color="Maroon">X1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">f</font> <a href="relat_1.html#K9">.:</a> <font color="Maroon">X2</font>
 <b>and </b><br/><a NAME="E2:103"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">X1</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E3:103"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">f</font> is <a href="funct_1.html#V2" target="_self">one-to-one</a>
 ;<br/>

<b>let </b><font color="Maroon">x</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="E4:103"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X1</font>
 ;<br/>

<a NAME="E5:103"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1" target="_self">.</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="relat_1.html#K9">.:</a> <font color="Maroon">X1</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:103"/><b>then </b>
 ex <font color="Olive">x2</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">x2</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> &amp; <font color="Olive">x2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X2</font> &amp; <font color="Maroon">f</font> <a href="funct_1.html#K1" target="_self">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1" target="_self">.</a> <font color="Olive">x2</font> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E7:103"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X2</font>
 <b>by </b><i>, , , </i>;<br/>


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