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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></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="E2:86"/><i><font color="Green">E52</font></i>: 
 <a href="substut1.html#K37" target="_self">CQC_Sub</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E3:86"/><i><font color="Green">E53</font></i>: 
for <font color="Olive">b<sub>1</sub></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">b<sub>1</sub></font> is <a href="substut1.html#V2" target="_self">Sub_VERUM</a> implies <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="cqc_lang.html#K9">VERUM</a>  ) &amp; ( <font color="Olive">b<sub>1</sub></font> is <a href="substut1.html#V4" target="_self">Sub_atomic</a> implies <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></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">b<sub>1</sub></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">b<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="substut1.html#K19" target="_self">`2</a> </span>)</span></span>)</span> ) &amp; ( <font color="Olive">b<sub>1</sub></font> is <a href="substut1.html#V5" target="_self">Sub_negative</a> implies <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K12">'not'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></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">b<sub>1</sub></font></span>)</span></span>)</span> ) &amp; ( <font color="Olive">b<sub>1</sub></font> is <a href="substut1.html#V6" target="_self">Sub_conjunctive</a> implies <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></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">b<sub>1</sub></font></span>)</span></span>)</span> <a href="qc_lang1.html#K13">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></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">b<sub>1</sub></font></span>)</span></span>)</span> ) &amp; ( <font color="Olive">b<sub>1</sub></font> is <a href="substut1.html#V7" target="_self">Sub_universal</a> implies <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="substut1.html#K36" target="_self">Quant</a> <font color="Olive">b<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></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">b<sub>1</sub></font></span>)</span></span>)</span> ) )
 <b>by </b><i><a class="ref" href="substut1.html#D38" target="_self">Def38</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>3</sub></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="E5:86"/><i><font color="Green">E54</font></i>: 
 <a href="substut1.html#K37" target="_self">CQC_Sub</a> <span class="p1">(<span class="default"><a href="substut1.html#K31" target="_self">Sub_the_scope_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="substut1.html#K31" target="_self">Sub_the_scope_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E6:86"/><i><font color="Green">E55</font></i>: 
for <font color="Olive">b<sub>1</sub></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">b<sub>1</sub></font> is <a href="substut1.html#V2" target="_self">Sub_VERUM</a> implies <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="cqc_lang.html#K9">VERUM</a>  ) &amp; ( <font color="Olive">b<sub>1</sub></font> is <a href="substut1.html#V4" target="_self">Sub_atomic</a> implies <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></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">b<sub>1</sub></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">b<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="substut1.html#K19" target="_self">`2</a> </span>)</span></span>)</span> ) &amp; ( <font color="Olive">b<sub>1</sub></font> is <a href="substut1.html#V5" target="_self">Sub_negative</a> implies <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K12">'not'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></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">b<sub>1</sub></font></span>)</span></span>)</span> ) &amp; ( <font color="Olive">b<sub>1</sub></font> is <a href="substut1.html#V6" target="_self">Sub_conjunctive</a> implies <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></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">b<sub>1</sub></font></span>)</span></span>)</span> <a href="qc_lang1.html#K13">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></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">b<sub>1</sub></font></span>)</span></span>)</span> ) &amp; ( <font color="Olive">b<sub>1</sub></font> is <a href="substut1.html#V7" target="_self">Sub_universal</a> implies <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="substut1.html#K36" target="_self">Quant</a> <font color="Olive">b<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></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">b<sub>1</sub></font></span>)</span></span>)</span> ) )
 <b>by </b><i><a class="ref" href="substut1.html#D38" target="_self">Def38</a></i>;<br/>
<a NAME="E7:86"/>
<font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="substut1.html#E3:86"><i><font color="Green">E53</font></i></a>, <a class="txt" href="substut1.html#E6:86"><i><font color="Green">E55</font></i></a>, <a class="txt" href="substut1.html#E69"><i><font color="Green">Lemma45</font></i></a></i>;<br/>
<b>hence </b><a NAME="E8:86"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="substut1.html#V7" target="_self">Sub_universal</a> implies  <a href="substut1.html#K37" target="_self">CQC_Sub</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="substut1.html#K36" target="_self">Quant</a> <font color="Maroon">c<sub>1</sub></font>,<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#K31" target="_self">Sub_the_scope_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="substut1.html#E2:86"><i><font color="Green">E52</font></i></a>, <a class="txt" href="substut1.html#E3:86"><i><font color="Green">E53</font></i></a>, <a class="txt" href="substut1.html#E5:86"><i><font color="Green">E54</font></i></a></i>;<br/>


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