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





<b>assume </b><b>that </b><br/><a NAME="E1:11"/><i><font color="Green">E16</font></i>: 
 <a href="funct_2.html#K1">Funcs</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>and </b><br/><a NAME="E2:11"/><i><font color="Green">E18</font></i>: 
( <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> &amp; <font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font> )
 ;<br/>

<b>let </b><font color="Maroon">f</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="funct_2.html#K1">Funcs</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font>;<br/>

<b>consider </b><font color="Maroon">g</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E4:11"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font>
 <b>and </b><br/><a NAME="E5:11"/><i><font color="Green">E31</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">g</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font> )
 <b>by </b><i>, <a class="ref" href="funct_2.html#D2">FUNCT_2:def 2</a></i>;<br/>
<a NAME="E6:11"/>
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">g</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font> )
 
<b>by </b><i>, , <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E7:11"/>
<font color="Maroon">f</font> is   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font>
 <b>by </b><i>, <a class="ref" href="relset_1.html#T11">RELSET_1:11</a></i>;<br/>


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