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<b>let </b><font color="Maroon" title="c2">A1</font>, <font color="Maroon" title="c3">A2</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:26_1_2"/><i><font color="Green" title="E21">A2</font></i>: 
for <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds <br/> ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A1</font> iff <font color="Olive" title="b1">x</font> is <a href="waybel15.html#V1" title="WAYBEL15:attr.1">atom</a> )
 <b>and </b><br/><a NAME="E2:26_1_2"/><i><font color="Green" title="E22">A3</font></i>: 
for <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds <br/> ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A2</font> iff <font color="Olive" title="b1">x</font> is <a href="waybel15.html#V1" title="WAYBEL15:attr.1">atom</a> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>thus </b><a NAME="E1:26_1_2_1"/>
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A1</font> implies <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A2</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_2_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:26_1_2_1_1"/><i><font color="Green" title="E23">A4</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A1</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c5">x'</font> = <font color="Maroon" title="c4">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> ;<br/>
<a NAME="E3:26_1_2_1_1"/>
<font color="Maroon" title="c5">x'</font> is <a href="waybel15.html#V1" title="WAYBEL15:attr.1">atom</a>
 
<b>by </b><i><a class="txt" href="waybel15.html#E1:26_1_2"><i><font color="Green" title="E21">A2</font></i></a>, <a class="txt" href="waybel15.html#E1:26_1_2_1_1"><i><font color="Green" title="E23">A4</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:26_1_2_1_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A2</font>
 <b>by </b><i><a class="txt" href="waybel15.html#E2:26_1_2"><i><font color="Green" title="E22">A3</font></i></a></i>;<br/>


</div><b>end;</b></div><b>thus </b><a NAME="E2:26_1_2_1"/>
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A2</font> implies <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A1</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_2_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:26_1_2_1_2"/><i><font color="Green" title="E23">A5</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A2</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c5">x'</font> = <font color="Maroon" title="c4">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> ;<br/>
<a NAME="E3:26_1_2_1_2"/>
<font color="Maroon" title="c5">x'</font> is <a href="waybel15.html#V1" title="WAYBEL15:attr.1">atom</a>
 
<b>by </b><i><a class="txt" href="waybel15.html#E2:26_1_2"><i><font color="Green" title="E22">A3</font></i></a>, <a class="txt" href="waybel15.html#E1:26_1_2_1_2"><i><font color="Green" title="E23">A5</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:26_1_2_1_2"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A1</font>
 <b>by </b><i><a class="txt" href="waybel15.html#E1:26_1_2"><i><font color="Green" title="E21">A2</font></i></a></i>;<br/>


</div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E4:26_1_2"/>
<font color="Maroon" title="c2">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A2</font>
 <b>by </b><i><a class="ref" href="tarski.html#T2" title="TARSKI:th.2">TARSKI:2</a></i>;<br/>


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