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<b>let </b><font color="Maroon" title="c2">x1</font>, <font color="Maroon" title="c3">x2</font> be   <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a>;<br/>



<b>assume </b><a NAME="E1:56_1_2"/><i><font color="Green" title="E32">A3</font></i>: 
(  ex <font color="Olive" title="b1">B</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a> ,<a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> </span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> ex <font color="Olive" title="b2">SQ</font> being   <a href="substut1.html#M1" title="SUBSTUT1:mode.1">second_Q_comp</a> of <font color="Olive" title="b1">B</font> st <br/>( <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <font color="Olive" title="b1">B</font>,<font color="Olive" title="b2">SQ</font> &amp; <font color="Olive" title="b1">B</font> <a href="substut1.html#K23" title="SUBSTUT1:func.23">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x1</font> &amp; <font color="Olive" title="b1">B</font> is <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a> ) &amp;  ex <font color="Olive" title="b1">B</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a> ,<a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> </span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> ex <font color="Olive" title="b2">SQ</font> being   <a href="substut1.html#M1" title="SUBSTUT1:mode.1">second_Q_comp</a> of <font color="Olive" title="b1">B</font> st <br/>( <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <font color="Olive" title="b1">B</font>,<font color="Olive" title="b2">SQ</font> &amp; <font color="Olive" title="b1">B</font> <a href="substut1.html#K23" title="SUBSTUT1:func.23">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x2</font> &amp; <font color="Olive" title="b1">B</font> is <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a> ) )
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">B1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a> ,<a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> </span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>, <font color="Maroon" title="c5">SQ1</font> being    <a href="substut1.html#M1" title="SUBSTUT1:mode.1">second_Q_comp</a> of <font color="Maroon" title="c4">B1</font><b> such that </b><br/><a NAME="E3:56_1_2"/><i><font color="Green" title="E33">A4</font></i>: 
( <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <font color="Maroon" title="c4">B1</font>,<font color="Maroon" title="c5">SQ1</font> &amp; <font color="Maroon" title="c4">B1</font> <a href="substut1.html#K23" title="SUBSTUT1:func.23">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x1</font> &amp; <font color="Maroon" title="c4">B1</font> is <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a> )
 ;<br/>
<b>consider </b><font color="Maroon" title="c6">B2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a> ,<a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> </span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>, <font color="Maroon" title="c7">SQ2</font> being    <a href="substut1.html#M1" title="SUBSTUT1:mode.1">second_Q_comp</a> of <font color="Maroon" title="c6">B2</font><b> such that </b><br/><a NAME="E5:56_1_2"/><i><font color="Green" title="E34">A5</font></i>: 
( <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <font color="Maroon" title="c6">B2</font>,<font color="Maroon" title="c7">SQ2</font> &amp; <font color="Maroon" title="c6">B2</font> <a href="substut1.html#K23" title="SUBSTUT1:func.23">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x2</font> &amp; <font color="Maroon" title="c6">B2</font> is <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a> )
 <b>by </b><i><a class="txt" href="substut1.html#E1:56_1_2"><i><font color="Green" title="E32">A3</font></i></a></i>;<br/>
<a NAME="E6:56_1_2"/><i><font color="Green" title="E35">A6</font></i>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">B1</font> <a href="substut1.html#K23" title="SUBSTUT1:func.23">`2</a> </span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">B1</font> <a href="substut1.html#K22" title="SUBSTUT1:func.22">`1</a> </span>)</span> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span></span>)</span>,<font color="Maroon" title="c5">SQ1</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">A</font>
 
<b>by </b><i><a class="txt" href="substut1.html#E3:56_1_2"><i><font color="Green" title="E33">A4</font></i></a>, <a class="ref" href="substut1.html#D24" target="_self" title="SUBSTUT1:def.24">Def24</a></i>;<br/>
<a NAME="E7:56_1_2"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">B2</font> <a href="substut1.html#K23" title="SUBSTUT1:func.23">`2</a> </span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">B2</font> <a href="substut1.html#K22" title="SUBSTUT1:func.22">`1</a> </span>)</span> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span></span>)</span>,<font color="Maroon" title="c7">SQ2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">A</font>
 
<b>by </b><i><a class="txt" href="substut1.html#E5:56_1_2"><i><font color="Green" title="E34">A5</font></i></a>, <a class="ref" href="substut1.html#D24" target="_self" title="SUBSTUT1:def.24">Def24</a></i>;<br/>
<a NAME="E8:56_1_2"/><b>then </b>
 <a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">B1</font> <a href="substut1.html#K23" title="SUBSTUT1:func.23">`2</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">B1</font> <a href="substut1.html#K22" title="SUBSTUT1:func.22">`1</a> </span>)</span> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">B2</font> <a href="substut1.html#K23" title="SUBSTUT1:func.23">`2</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">B2</font> <a href="substut1.html#K22" title="SUBSTUT1:func.22">`1</a> </span>)</span> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="substut1.html#E6:56_1_2"><i><font color="Green" title="E35">A6</font></i></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/>
<b>hence </b><a NAME="E9:56_1_2"/>
<font color="Maroon" title="c2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x2</font>
 <b>by </b><i><a class="txt" href="substut1.html#E3:56_1_2"><i><font color="Green" title="E33">A4</font></i></a>, <a class="txt" href="substut1.html#E5:56_1_2"><i><font color="Green" title="E34">A5</font></i></a>, <a class="ref" href="qc_lang2.html#T6" title="QC_LANG2:th.6">QC_LANG2:6</a></i>;<br/>


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