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





<b>assume </b><a NAME="E1:92"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1" target="_self">Funcs</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font>
 ;<br/>

<a NAME="E2:92"/><b>then </b><i><font color="Green">E21</font></i>: 
(  not <font color="Maroon">Y</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  or  not <font color="Maroon">X</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i/>;<br/>
<a NAME="E3:92"/>
 ex <font color="Olive">f'</font> being  <a href="funct_1.html#NM1">Function</a> st <br/>( <font color="Olive">f'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Olive">f'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Olive">f'</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font> )
 
<b>by </b><i><a class="ref" href="funct_2.html#T7" target="_self">Th7</a>, </i>;<br/>
<b>hence </b><a NAME="E4:92"/>
<font color="Maroon">f</font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font>,<font color="Maroon">Y</font>
 <b>by </b><i>, , <a class="ref" href="relset_1.html#T11">RELSET_1:11</a></i>;<br/>


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