<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">G</font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">H1</font> be  <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">G</font>, <font color="Maroon">H2</font> be  <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">G</font>;<br/>



<b>thus </b><a NAME="E1:114"/>
( <font color="Maroon">H1</font> <a href="hidden.html#R2">in</a>  <a href="group_3.html#K9" target="_self">con_class</a> <font color="Maroon">H2</font> implies <font color="Maroon">H1</font>,<font color="Maroon">H2</font> <a href="group_3.html#R6" target="_self">are_conjugated</a>  )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="114_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:114_1"/>
<font color="Maroon">H1</font> <a href="hidden.html#R2">in</a>  <a href="group_3.html#K9" target="_self">con_class</a> <font color="Maroon">H2</font>
 ;<br/>

<a NAME="E2:114_1"/><b>then </b>
 ex <font color="Olive">H3</font> being <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">G</font> st <br/>( <font color="Maroon">H1</font> <a href="group_2.html#R1">=</a> <font color="Olive">H3</font> &amp; <font color="Maroon">H2</font>,<font color="Olive">H3</font> <a href="group_3.html#R6" target="_self">are_conjugated</a>  )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:114_1"/>
<font color="Maroon">H1</font>,<font color="Maroon">H2</font> <a href="group_3.html#R6" target="_self">are_conjugated</a> 
 ;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:114"/>
<font color="Maroon">H1</font>,<font color="Maroon">H2</font> <a href="group_3.html#R6" target="_self">are_conjugated</a> 
 ;<br/>

<b>hence </b><a NAME="E3:114"/>
<font color="Maroon">H1</font> <a href="hidden.html#R2">in</a>  <a href="group_3.html#K9" target="_self">con_class</a> <font color="Maroon">H2</font>
 <b>by </b><i/>;<br/>


</div>
