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<b>let </b><font color="Maroon">G</font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">H</font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">h</font> be   <a href="group_6.html#NM2">Homomorphism</a> of <font color="Maroon">G</font>,<font color="Maroon">H</font>;<br/>





<b>assume </b><a NAME="E1:82"/>
<font color="Maroon">h</font> <a href="group_6.html#NR3" target="_self">is_isomorphism</a> 
 ;<br/>

<a NAME="E2:82"/><b>then </b>
<font color="Maroon">h</font> <a href="group_6.html#NR2" target="_self">is_epimorphism</a> 
 
<b>by </b><i><a class="ref" href="group_6.html#T8" target="_self">Th8</a></i>;<br/>
<b>hence </b><a NAME="E3:82"/>
(  <a href="relset_1.html#K4">dom</a> <font color="Maroon">h</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">h</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H</font> )
 <b>by </b><i>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>


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