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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">a</font>, <font color="Maroon" title="c3">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>;<br/>





<b>thus </b><a NAME="E1:83"/>
( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="group_3.html#K7" title="GROUP_3:func.7">con_class</a> <font color="Maroon" title="c3">b</font> implies <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="group_3.html#R2" title="GROUP_3:pred.2">are_conjugated</a>  )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="83_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:83_1"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="group_3.html#K7" title="GROUP_3:func.7">con_class</a> <font color="Maroon" title="c3">b</font>
 ;<br/>

<a NAME="E2:83_1"/><b>then </b>
 ex <font color="Olive" title="b1">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font> st <br/>( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">c</font> &amp; <font color="Maroon" title="c3">b</font>,<font color="Olive" title="b1">c</font> <a href="group_3.html#R2" title="GROUP_3:pred.2">are_conjugated</a>  )
 
<b>by </b><i><a class="ref" href="group_3.html#T95" target="_self" title="GROUP_3:th.95">Th95</a></i>;<br/>
<b>hence </b><a NAME="E3:83_1"/>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="group_3.html#R2" title="GROUP_3:pred.2">are_conjugated</a> 
 ;<br/>


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

<b>assume </b><a NAME="E2:83"/>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="group_3.html#R2" title="GROUP_3:pred.2">are_conjugated</a> 
 ;<br/>

<b>hence </b><a NAME="E3:83"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="group_3.html#K7" title="GROUP_3:func.7">con_class</a> <font color="Maroon" title="c3">b</font>
 <b>by </b><i><a class="ref" href="group_3.html#T95" target="_self" title="GROUP_3:th.95">Th95</a></i>;<br/>


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