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<b>let </b><font color="Maroon">S</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="substut1.html#K16" target="_self">QC-Sub-WFF</a> ;<br/>

<b>consider </b><font color="Maroon">F</font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="substut1.html#K16" target="_self">QC-Sub-WFF</a> , <a href="qc_lang1.html#K8">QC-WFF</a> <b> such that </b><br/><a NAME="E2:82"/><i><font color="Green">E40</font></i>: 
 <a href="substut1.html#K37" target="_self">CQC_Sub</a> <font color="Maroon">S</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">S</font>
 <b>and </b><br/><a NAME="E3:82"/><i><font color="Green">E43</font></i>: 
for <font color="Olive">S'</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="substut1.html#K16" target="_self">QC-Sub-WFF</a>  holds <br/> ( ( <font color="Olive">S'</font> is <a href="substut1.html#V2" target="_self">Sub_VERUM</a> implies <font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Olive">S'</font> <a href="hidden.html#R1">=</a>  <a href="cqc_lang.html#K9">VERUM</a>  ) &amp; ( <font color="Olive">S'</font> is <a href="substut1.html#V4" target="_self">Sub_atomic</a> implies <font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Olive">S'</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K15">the_pred_symbol_of</a> <span class="p2">(<span class="default"><font color="Olive">S'</font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span> <a href="qc_lang1.html#K9">!</a> <span class="p1">(<span class="default"><a href="substut1.html#K3" target="_self">CQC_Subst</a> <span class="p2">(<span class="default"><a href="substut1.html#K26" target="_self">Sub_the_arguments_of</a> <font color="Olive">S'</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive">S'</font> <a href="substut1.html#K19" target="_self">`2</a> </span>)</span></span>)</span> ) &amp; ( <font color="Olive">S'</font> is <a href="substut1.html#V5" target="_self">Sub_negative</a> implies <font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Olive">S'</font> <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K12">'not'</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="substut1.html#K27" target="_self">Sub_the_argument_of</a> <font color="Olive">S'</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive">S'</font> is <a href="substut1.html#V6" target="_self">Sub_conjunctive</a> implies <font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Olive">S'</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="substut1.html#K28" target="_self">Sub_the_left_argument_of</a> <font color="Olive">S'</font></span>)</span></span>)</span> <a href="qc_lang1.html#K13">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="substut1.html#K29" target="_self">Sub_the_right_argument_of</a> <font color="Olive">S'</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive">S'</font> is <a href="substut1.html#V7" target="_self">Sub_universal</a> implies <font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Olive">S'</font> <a href="hidden.html#R1">=</a>  <a href="substut1.html#K36" target="_self">Quant</a> <font color="Olive">S'</font>,<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="substut1.html#K31" target="_self">Sub_the_scope_of</a> <font color="Olive">S'</font></span>)</span></span>)</span> ) )
 <b>by </b><i><a class="txt" href="substut1.html#E6:82"><i><font color="Green">E46</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">G</font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="substut1.html#K16" target="_self">QC-Sub-WFF</a> , <a href="qc_lang1.html#K8">QC-WFF</a> <b> such that </b><br/><a NAME="E5:82"/><i><font color="Green">E45</font></i>: 
 <a href="substut1.html#K37" target="_self">CQC_Sub</a> <span class="p1">(<span class="default"><a href="substut1.html#K27" target="_self">Sub_the_argument_of</a> <font color="Maroon">S</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="substut1.html#K27" target="_self">Sub_the_argument_of</a> <font color="Maroon">S</font></span>)</span>
 <b>and </b><br/><a NAME="E6:82"/><i><font color="Green">E46</font></i>: 
for <font color="Olive">S'</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="substut1.html#K16" target="_self">QC-Sub-WFF</a>  holds <br/> ( ( <font color="Olive">S'</font> is <a href="substut1.html#V2" target="_self">Sub_VERUM</a> implies <font color="Maroon">G</font> <a href="funct_2.html#K3">.</a> <font color="Olive">S'</font> <a href="hidden.html#R1">=</a>  <a href="cqc_lang.html#K9">VERUM</a>  ) &amp; ( <font color="Olive">S'</font> is <a href="substut1.html#V4" target="_self">Sub_atomic</a> implies <font color="Maroon">G</font> <a href="funct_2.html#K3">.</a> <font color="Olive">S'</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K15">the_pred_symbol_of</a> <span class="p2">(<span class="default"><font color="Olive">S'</font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span> <a href="qc_lang1.html#K9">!</a> <span class="p1">(<span class="default"><a href="substut1.html#K3" target="_self">CQC_Subst</a> <span class="p2">(<span class="default"><a href="substut1.html#K26" target="_self">Sub_the_arguments_of</a> <font color="Olive">S'</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive">S'</font> <a href="substut1.html#K19" target="_self">`2</a> </span>)</span></span>)</span> ) &amp; ( <font color="Olive">S'</font> is <a href="substut1.html#V5" target="_self">Sub_negative</a> implies <font color="Maroon">G</font> <a href="funct_2.html#K3">.</a> <font color="Olive">S'</font> <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K12">'not'</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="substut1.html#K27" target="_self">Sub_the_argument_of</a> <font color="Olive">S'</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive">S'</font> is <a href="substut1.html#V6" target="_self">Sub_conjunctive</a> implies <font color="Maroon">G</font> <a href="funct_2.html#K3">.</a> <font color="Olive">S'</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="substut1.html#K28" target="_self">Sub_the_left_argument_of</a> <font color="Olive">S'</font></span>)</span></span>)</span> <a href="qc_lang1.html#K13">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="substut1.html#K29" target="_self">Sub_the_right_argument_of</a> <font color="Olive">S'</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive">S'</font> is <a href="substut1.html#V7" target="_self">Sub_universal</a> implies <font color="Maroon">G</font> <a href="funct_2.html#K3">.</a> <font color="Olive">S'</font> <a href="hidden.html#R1">=</a>  <a href="substut1.html#K36" target="_self">Quant</a> <font color="Olive">S'</font>,<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="substut1.html#K31" target="_self">Sub_the_scope_of</a> <font color="Olive">S'</font></span>)</span></span>)</span> ) )
 <b>by </b><i><a class="txt" href="substut1.html#E6:82"><i><font color="Green">E46</font></i></a></i>;<br/>
<a NAME="E7:82"/>
<font color="Maroon">F</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">G</font>
 
<b>by </b><i>, , <a class="txt" href="substut1.html#E5:82"><i><font color="Green">E45</font></i></a></i>;<br/>
<b>hence </b><a NAME="E8:82"/>
( <font color="Maroon">S</font> is <a href="substut1.html#V5" target="_self">Sub_negative</a> implies  <a href="substut1.html#K37" target="_self">CQC_Sub</a> <font color="Maroon">S</font> <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K12">'not'</a> <span class="p1">(<span class="default"><a href="substut1.html#K37" target="_self">CQC_Sub</a> <span class="p2">(<span class="default"><a href="substut1.html#K27" target="_self">Sub_the_argument_of</a> <font color="Maroon">S</font></span>)</span></span>)</span> )
 <b>by </b><i>, , </i>;<br/>


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