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<span class="kw">let </span><font color="Maroon" title="c1">B</font> be    <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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">SQ</font> being   <a href="substut1.html#M1" title="SUBSTUT1:mode.1">second_Q_comp</a> of <font color="Maroon" title="c1">B</font>  st <font color="Maroon" title="c1">B</font> is  <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a>  holds <br/> <a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <font color="Maroon" title="c1">B</font>,<font color="Olive" title="b1">SQ</font> is  <a href="substut1.html#V7" title="SUBSTUT1:attr.7">Sub_universal</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">SQ</font> be    <a href="substut1.html#M1" title="SUBSTUT1:mode.1">second_Q_comp</a> of <font color="Maroon" title="c1">B</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">B</font> is  <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a>  implies  <a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">SQ</font> is  <a href="substut1.html#V7" title="SUBSTUT1:attr.7">Sub_universal</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:60"/><span class="lab"><font color="Green" title="E34">A1</font></span>: 
<font color="Maroon" title="c1">B</font> is  <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">SQ</font> is  <a href="substut1.html#V7" title="SUBSTUT1:attr.7">Sub_universal</a> </span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c1">B</font>
; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="substut1.html#D28" target="_self" title="SUBSTUT1:def.28">SUBSTUT1:def 28</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">SQ</font> being   <a href="substut1.html#M1" title="SUBSTUT1:mode.1">second_Q_comp</a> of <font color="Maroon" title="c1">B</font> st <br/>(  <a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">SQ</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="c1">B</font>,<font color="Olive" title="b1">SQ</font> &amp; <font color="Maroon" title="c1">B</font> is  <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a>  )</span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c2">SQ</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">SQ</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="c1">B</font>,<font color="Maroon" title="c2">SQ</font> &amp; <font color="Maroon" title="c1">B</font> is  <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E2:60"/>
(  <a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">SQ</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="c1">B</font>,<font color="Maroon" title="c2">SQ</font> &amp; <font color="Maroon" title="c1">B</font> is  <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:60"><span class="lab"><font color="Green" title="E34">A1</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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