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<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:96_2_1_1"/>
<font color="Maroon" title="c2">X</font> <a href="roughs_1.html#R5" title="ROUGHS_1:pred.5">=^</a> <font color="Maroon" title="c3">Y</font>
 ;<br/><a NAME="E2:96_2_1_1"/><b>then </b>
 <a href="roughs_1.html#K4" title="ROUGHS_1:func.4">UAp</a> <font color="Maroon" title="c2">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="roughs_1.html#K4" title="ROUGHS_1:func.4">UAp</a> <font color="Maroon" title="c3">Y</font>
 <b>by </b><i><a class="ref" href="roughs_1.html#D15" target="_self" title="ROUGHS_1:def.15">Def15</a></i>;<br/><b>hence </b><a NAME="E3:96_2_1_1"/>
( <font color="Maroon" title="c2">X</font> <a href="roughs_1.html#R2" title="ROUGHS_1:pred.2">c=^</a> <font color="Maroon" title="c3">Y</font> &amp; <font color="Maroon" title="c3">Y</font> <a href="roughs_1.html#R2" title="ROUGHS_1:pred.2">c=^</a> <font color="Maroon" title="c2">X</font> )
 <b>by </b><i><a class="ref" href="roughs_1.html#D12" target="_self" title="ROUGHS_1:def.12">Def12</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:96_2_1"/>
( <font color="Maroon" title="c2">X</font> <a href="roughs_1.html#R2" title="ROUGHS_1:pred.2">c=^</a> <font color="Maroon" title="c3">Y</font> &amp; <font color="Maroon" title="c3">Y</font> <a href="roughs_1.html#R2" title="ROUGHS_1:pred.2">c=^</a> <font color="Maroon" title="c2">X</font> )
 ;<br/>

<a NAME="E3:96_2_1"/><b>then </b>
(  <a href="roughs_1.html#K4" title="ROUGHS_1:func.4">UAp</a> <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="roughs_1.html#K4" title="ROUGHS_1:func.4">UAp</a> <font color="Maroon" title="c3">Y</font> &amp;  <a href="roughs_1.html#K4" title="ROUGHS_1:func.4">UAp</a> <font color="Maroon" title="c3">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="roughs_1.html#K4" title="ROUGHS_1:func.4">UAp</a> <font color="Maroon" title="c2">X</font> )
 
<b>by </b><i><a class="ref" href="roughs_1.html#D12" target="_self" title="ROUGHS_1:def.12">Def12</a></i>;<br/>
<a NAME="E4:96_2_1"/><b>then </b>
 <a href="roughs_1.html#K4" title="ROUGHS_1:func.4">UAp</a> <font color="Maroon" title="c2">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="roughs_1.html#K4" title="ROUGHS_1:func.4">UAp</a> <font color="Maroon" title="c3">Y</font>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>;<br/>
<b>hence </b><a NAME="E5:96_2_1"/>
<font color="Maroon" title="c2">X</font> <a href="roughs_1.html#R5" title="ROUGHS_1:pred.5">=^</a> <font color="Maroon" title="c3">Y</font>
 <b>by </b><i><a class="ref" href="roughs_1.html#D15" target="_self" title="ROUGHS_1:def.15">Def15</a></i>;<br/>


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