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<b>let </b><font color="Maroon" title="c1">G</font> be   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>;<br/><b>let </b><font color="Maroon" title="c2">H1</font>, <font color="Maroon" title="c3">H2</font> be  <a href="group_1.html#V1" title="GROUP_1:attr.1">strict</a>  <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font>;<br/>



<b>thus </b><a NAME="E1:114"/>
( <font color="Maroon" title="c2">H1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="group_3.html#K9" title="GROUP_3:func.9">con_class</a> <font color="Maroon" title="c3">H2</font> implies <font color="Maroon" title="c2">H1</font>,<font color="Maroon" title="c3">H2</font> <a href="group_3.html#R6" title="GROUP_3:pred.6">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" title="c2">H1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="group_3.html#K9" title="GROUP_3:func.9">con_class</a> <font color="Maroon" title="c3">H2</font>
 ;<br/>

<a NAME="E2:114_1"/><b>then </b>
 ex <font color="Olive" title="b1">H3</font> being <a href="group_1.html#V1" title="GROUP_1:attr.1">strict</a>  <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font> st <br/>( <font color="Maroon" title="c2">H1</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> <font color="Olive" title="b1">H3</font> &amp; <font color="Maroon" title="c3">H2</font>,<font color="Olive" title="b1">H3</font> <a href="group_3.html#R6" title="GROUP_3:pred.6">are_conjugated</a>  )
 
<b>by </b><i><a class="ref" href="group_3.html#D12" target="_self" title="GROUP_3:def.12">Def12</a></i>;<br/>
<b>hence </b><a NAME="E3:114_1"/>
<font color="Maroon" title="c2">H1</font>,<font color="Maroon" title="c3">H2</font> <a href="group_3.html#R6" title="GROUP_3:pred.6">are_conjugated</a> 
 ;<br/>


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

<b>assume </b><a NAME="E2:114"/>
<font color="Maroon" title="c2">H1</font>,<font color="Maroon" title="c3">H2</font> <a href="group_3.html#R6" title="GROUP_3:pred.6">are_conjugated</a> 
 ;<br/>

<b>hence </b><a NAME="E3:114"/>
<font color="Maroon" title="c2">H1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="group_3.html#K9" title="GROUP_3:func.9">con_class</a> <font color="Maroon" title="c3">H2</font>
 <b>by </b><i><a class="ref" href="group_3.html#D12" target="_self" title="GROUP_3:def.12">Def12</a></i>;<br/>


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