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<b>let </b><font color="Maroon" title="c1">S</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">S</font> is <a href="substut1.html#V7" title="SUBSTUT1:attr.7">Sub_universal</a> implies  <a href="substut1.html#K37" title="SUBSTUT1:func.37">CQC_Sub</a> <font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut1.html#K36" title="SUBSTUT1:func.36">Quant</a> <font color="Maroon" title="c1">S</font>,<span class="p1">(<span class="default"><a href="substut1.html#K37" title="SUBSTUT1:func.37">CQC_Sub</a> <span class="p2">(<span class="default"><a href="substut1.html#K31" title="SUBSTUT1:func.31">Sub_the_scope_of</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span> )</span><br/>

<b>consider </b><font color="Maroon" title="c2">F</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a> , <a href="qc_lang1.html#K8" title="QC_LANG1:func.8">QC-WFF</a> <b> such that </b><br/><a NAME="E2:86"/><i><font color="Green" title="E52">A1</font></i>: 
 <a href="substut1.html#K37" title="SUBSTUT1:func.37">CQC_Sub</a> <font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c1">S</font>
 <b>and </b><br/><a NAME="E3:86"/><i><font color="Green" title="E53">A2</font></i>: 
for <font color="Olive" title="b1">S'</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>  holds <br/> ( ( <font color="Olive" title="b1">S'</font> is <a href="substut1.html#V2" title="SUBSTUT1:attr.2">Sub_VERUM</a> implies <font color="Maroon" title="c2">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">S'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_lang.html#K6" title="CQC_LANG:func.6">VERUM</a>  ) &amp; ( <font color="Olive" title="b1">S'</font> is <a href="substut1.html#V4" title="SUBSTUT1:attr.4">Sub_atomic</a> implies <font color="Maroon" title="c2">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">S'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K15" title="QC_LANG1:func.15">the_pred_symbol_of</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">S'</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span></span>)</span> <a href="qc_lang1.html#K9" title="QC_LANG1:func.9">!</a> <span class="p1">(<span class="default"><a href="substut1.html#K3" title="SUBSTUT1:func.3">CQC_Subst</a> <span class="p2">(<span class="default"><a href="substut1.html#K26" title="SUBSTUT1:func.26">Sub_the_arguments_of</a> <font color="Olive" title="b1">S'</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">S'</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a> </span>)</span></span>)</span> ) &amp; ( <font color="Olive" title="b1">S'</font> is <a href="substut1.html#V5" title="SUBSTUT1:attr.5">Sub_negative</a> implies <font color="Maroon" title="c2">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">S'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><a href="substut1.html#K27" title="SUBSTUT1:func.27">Sub_the_argument_of</a> <font color="Olive" title="b1">S'</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive" title="b1">S'</font> is <a href="substut1.html#V6" title="SUBSTUT1:attr.6">Sub_conjunctive</a> implies <font color="Maroon" title="c2">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">S'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><a href="substut1.html#K28" title="SUBSTUT1:func.28">Sub_the_left_argument_of</a> <font color="Olive" title="b1">S'</font></span>)</span></span>)</span> <a href="qc_lang1.html#K13" title="QC_LANG1:func.13">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><a href="substut1.html#K29" title="SUBSTUT1:func.29">Sub_the_right_argument_of</a> <font color="Olive" title="b1">S'</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive" title="b1">S'</font> is <a href="substut1.html#V7" title="SUBSTUT1:attr.7">Sub_universal</a> implies <font color="Maroon" title="c2">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">S'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut1.html#K36" title="SUBSTUT1:func.36">Quant</a> <font color="Olive" title="b1">S'</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><a href="substut1.html#K31" title="SUBSTUT1:func.31">Sub_the_scope_of</a> <font color="Olive" title="b1">S'</font></span>)</span></span>)</span> ) )
 <b>by </b><i><a class="ref" href="substut1.html#D38" target="_self" title="SUBSTUT1:def.38">Def38</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c3">G</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a> , <a href="qc_lang1.html#K8" title="QC_LANG1:func.8">QC-WFF</a> <b> such that </b><br/><a NAME="E5:86"/><i><font color="Green" title="E54">A3</font></i>: 
 <a href="substut1.html#K37" title="SUBSTUT1:func.37">CQC_Sub</a> <span class="p1">(<span class="default"><a href="substut1.html#K31" title="SUBSTUT1:func.31">Sub_the_scope_of</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="substut1.html#K31" title="SUBSTUT1:func.31">Sub_the_scope_of</a> <font color="Maroon" title="c1">S</font></span>)</span>
 <b>and </b><br/><a NAME="E6:86"/><i><font color="Green" title="E55">A4</font></i>: 
for <font color="Olive" title="b1">S'</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>  holds <br/> ( ( <font color="Olive" title="b1">S'</font> is <a href="substut1.html#V2" title="SUBSTUT1:attr.2">Sub_VERUM</a> implies <font color="Maroon" title="c3">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">S'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_lang.html#K6" title="CQC_LANG:func.6">VERUM</a>  ) &amp; ( <font color="Olive" title="b1">S'</font> is <a href="substut1.html#V4" title="SUBSTUT1:attr.4">Sub_atomic</a> implies <font color="Maroon" title="c3">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">S'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K15" title="QC_LANG1:func.15">the_pred_symbol_of</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">S'</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span></span>)</span> <a href="qc_lang1.html#K9" title="QC_LANG1:func.9">!</a> <span class="p1">(<span class="default"><a href="substut1.html#K3" title="SUBSTUT1:func.3">CQC_Subst</a> <span class="p2">(<span class="default"><a href="substut1.html#K26" title="SUBSTUT1:func.26">Sub_the_arguments_of</a> <font color="Olive" title="b1">S'</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">S'</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a> </span>)</span></span>)</span> ) &amp; ( <font color="Olive" title="b1">S'</font> is <a href="substut1.html#V5" title="SUBSTUT1:attr.5">Sub_negative</a> implies <font color="Maroon" title="c3">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">S'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><a href="substut1.html#K27" title="SUBSTUT1:func.27">Sub_the_argument_of</a> <font color="Olive" title="b1">S'</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive" title="b1">S'</font> is <a href="substut1.html#V6" title="SUBSTUT1:attr.6">Sub_conjunctive</a> implies <font color="Maroon" title="c3">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">S'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><a href="substut1.html#K28" title="SUBSTUT1:func.28">Sub_the_left_argument_of</a> <font color="Olive" title="b1">S'</font></span>)</span></span>)</span> <a href="qc_lang1.html#K13" title="QC_LANG1:func.13">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><a href="substut1.html#K29" title="SUBSTUT1:func.29">Sub_the_right_argument_of</a> <font color="Olive" title="b1">S'</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive" title="b1">S'</font> is <a href="substut1.html#V7" title="SUBSTUT1:attr.7">Sub_universal</a> implies <font color="Maroon" title="c3">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">S'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut1.html#K36" title="SUBSTUT1:func.36">Quant</a> <font color="Olive" title="b1">S'</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><a href="substut1.html#K31" title="SUBSTUT1:func.31">Sub_the_scope_of</a> <font color="Olive" title="b1">S'</font></span>)</span></span>)</span> ) )
 <b>by </b><i><a class="ref" href="substut1.html#D38" target="_self" title="SUBSTUT1:def.38">Def38</a></i>;<br/>
<a NAME="E7:86"/>
<font color="Maroon" title="c2">F</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">G</font>
 
<b>by </b><i><a class="txt" href="#E3:86"><i><font color="Green" title="E53">A2</font></i></a>, <a class="txt" href="#E6:86"><i><font color="Green" title="E55">A4</font></i></a>, <a class="txt" href="substut1.html#E69"><i><font color="Green" title="E45">Lm5</font></i></a></i>;<br/>
<b>hence </b><a NAME="E8:86"/>
( <font color="Maroon" title="c1">S</font> is <a href="substut1.html#V7" title="SUBSTUT1:attr.7">Sub_universal</a> implies  <a href="substut1.html#K37" title="SUBSTUT1:func.37">CQC_Sub</a> <font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut1.html#K36" title="SUBSTUT1:func.36">Quant</a> <font color="Maroon" title="c1">S</font>,<span class="p1">(<span class="default"><a href="substut1.html#K37" title="SUBSTUT1:func.37">CQC_Sub</a> <span class="p2">(<span class="default"><a href="substut1.html#K31" title="SUBSTUT1:func.31">Sub_the_scope_of</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="#E2:86"><i><font color="Green" title="E52">A1</font></i></a>, <a class="txt" href="#E3:86"><i><font color="Green" title="E53">A2</font></i></a>, <a class="txt" href="#E5:86"><i><font color="Green" title="E54">A3</font></i></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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