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<b>let </b><font color="Maroon" title="c1">p1</font>, <font color="Maroon" title="c2">p2</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qc_lang1.html#K8" title="QC_LANG1:func.8">QC-WFF</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">x2</font>, <font color="Olive" title="b3">y1</font>, <font color="Olive" title="b4">y2</font> being  <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a>  st  <a href="qc_lang2.html#K7" title="QC_LANG2:func.7">Ex</a> <font color="Olive" title="b1">x1</font>,<font color="Olive" title="b3">y1</font>,<font color="Maroon" title="c1">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang2.html#K7" title="QC_LANG2:func.7">Ex</a> <font color="Olive" title="b2">x2</font>,<font color="Olive" title="b4">y2</font>,<font color="Maroon" title="c2">p2</font> holds <br/>( <font color="Olive" title="b1">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">x2</font> &amp; <font color="Olive" title="b3">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">y2</font> &amp; <font color="Maroon" title="c1">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p2</font> )</span><br/><b>let </b><font color="Maroon" title="c3">x1</font>, <font color="Maroon" title="c4">x2</font>, <font color="Maroon" title="c5">y1</font>, <font color="Maroon" title="c6">y2</font> be   <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="qc_lang2.html#K7" title="QC_LANG2:func.7">Ex</a> <font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang2.html#K7" title="QC_LANG2:func.7">Ex</a> <font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c6">y2</font>,<font color="Maroon" title="c2">p2</font> implies ( <font color="Maroon" title="c3">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x2</font> &amp; <font color="Maroon" title="c5">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">y2</font> &amp; <font color="Maroon" title="c1">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p2</font> ) )</span><br/>





<b>assume </b><a NAME="E1:17"/><i><font color="Green" title="E12">A1</font></i>: 
 <a href="qc_lang2.html#K7" title="QC_LANG2:func.7">Ex</a> <font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang2.html#K7" title="QC_LANG2:func.7">Ex</a> <font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c6">y2</font>,<font color="Maroon" title="c2">p2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x2</font> &amp; <font color="Maroon" title="c5">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">y2</font> &amp; <font color="Maroon" title="c1">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p2</font> )</span><br/>

<b>thus </b><a NAME="E2:17"/>
<font color="Maroon" title="c3">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x2</font>
 <b>by </b><i><a class="txt" href="qc_lang2.html#E1:17"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="qc_lang2.html#T19" target="_self" title="QC_LANG2:th.19">Th19</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">y2</font> &amp; <font color="Maroon" title="c1">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p2</font> )</span><br/>

<a NAME="E3:17"/>
 <a href="qc_lang2.html#K5" title="QC_LANG2:func.5">Ex</a> <font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang2.html#K5" title="QC_LANG2:func.5">Ex</a> <font color="Maroon" title="c6">y2</font>,<font color="Maroon" title="c2">p2</font>
 
<b>by </b><i><a class="txt" href="qc_lang2.html#E1:17"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="qc_lang2.html#T19" target="_self" title="QC_LANG2:th.19">Th19</a></i>;<br/>
<b>hence </b><a NAME="E4:17"/>
( <font color="Maroon" title="c5">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">y2</font> &amp; <font color="Maroon" title="c1">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p2</font> )
 <b>by </b><i><a class="ref" href="qc_lang2.html#T19" target="_self" title="QC_LANG2:th.19">Th19</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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