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<b>let </b><font color="Maroon" title="c1">B</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds   <a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <font color="Olive" title="b1">A</font>,<font color="Maroon" title="c1">B</font> is    <a href="fraenkel.html#M1" title="FRAENKEL:mode.1">FUNCTION_DOMAIN</a> of <font color="Olive" title="b1">A</font>,<font color="Maroon" title="c1">B</font></span><br/><b>let </b><font color="Maroon" title="c2">A</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c1">B</font> is    <a href="fraenkel.html#M1" title="FRAENKEL:mode.1">FUNCTION_DOMAIN</a> of <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c1">B</font></span><br/>



<a NAME="E1:31"/><i><font color="Green" title="E8">A1</font></i>: 
 <a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c1">B</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="funct_2.html#T11" title="FUNCT_2:th.11">FUNCT_2:11</a></i>;<br/>
<a NAME="E2:31"/><b>then </b>
for <font color="Olive" title="b1">f</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c1">B</font> holds  <font color="Olive" title="b1">f</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c1">B</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#T121" title="FUNCT_2:th.121">FUNCT_2:121</a></i>;<br/>
<b>hence </b><a NAME="E3:31"/>
 <a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c1">B</font> is    <a href="fraenkel.html#M1" title="FRAENKEL:mode.1">FUNCTION_DOMAIN</a> of <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c1">B</font>
 <b>by </b><i><a class="txt" href="fraenkel.html#E1:31"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="fraenkel.html#D2" target="_self" title="FRAENKEL:def.2">Def2</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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