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<b>let </b><font color="Maroon" title="c1">S1</font>, <font color="Maroon" title="c2">S2</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">S1</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">S2</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  implies  <a href="substut1.html#K28" title="SUBSTUT1:func.28">Sub_the_left_argument_of</a> <span class="p1">(<span class="default"><a href="substut1.html#K21" title="SUBSTUT1:func.21">Sub_&amp;</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">S1</font> )</span><br/>



<b>assume </b><a NAME="E1:63"/><i><font color="Green" title="E36">A1</font></i>: 
<font color="Maroon" title="c1">S1</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">S2</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="substut1.html#K28" title="SUBSTUT1:func.28">Sub_the_left_argument_of</a> <span class="p1">(<span class="default"><a href="substut1.html#K21" title="SUBSTUT1:func.21">Sub_&amp;</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">S1</font></span><br/>

<a NAME="E2:63"/><b>then </b>
 <a href="substut1.html#K21" title="SUBSTUT1:func.21">Sub_&amp;</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font> is <a href="substut1.html#V6" title="SUBSTUT1:attr.6">Sub_conjunctive</a>
 
<b>by </b><i><a class="ref" href="substut1.html#T13" target="_self" title="SUBSTUT1:th.13">Th13</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c3">S2'</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a> <b> such that </b><br/><a NAME="E4:63"/><i><font color="Green" title="E37">A2</font></i>: 
(  <a href="substut1.html#K21" title="SUBSTUT1:func.21">Sub_&amp;</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut1.html#K21" title="SUBSTUT1:func.21">Sub_&amp;</a> <span class="p1">(<span class="default"><a href="substut1.html#K28" title="SUBSTUT1:func.28">Sub_the_left_argument_of</a> <span class="p2">(<span class="default"><a href="substut1.html#K21" title="SUBSTUT1:func.21">Sub_&amp;</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">S2'</font> &amp; <span class="p1">(<span class="default"><a href="substut1.html#K28" title="SUBSTUT1:func.28">Sub_the_left_argument_of</a> <span class="p2">(<span class="default"><a href="substut1.html#K21" title="SUBSTUT1:func.21">Sub_&amp;</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font></span>)</span></span>)</span> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">S2'</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  )
 <b>by </b><i><a class="ref" href="substut1.html#D31" target="_self" title="SUBSTUT1:def.31">Def31</a></i>;<br/>
<b>thus </b><a NAME="E5:63"/>
 <a href="substut1.html#K28" title="SUBSTUT1:func.28">Sub_the_left_argument_of</a> <span class="p1">(<span class="default"><a href="substut1.html#K21" title="SUBSTUT1:func.21">Sub_&amp;</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">S1</font>
 <b>by </b><i><a class="txt" href="#E1:63"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="#E4:63"><i><font color="Green" title="E37">A2</font></i></a>, <a class="ref" href="substut1.html#T17" target="_self" title="SUBSTUT1:th.17">Th17</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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