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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> ;<br/>

<a NAME="E1:73"/>
( ( <font color="Maroon" title="c1">S</font> is <a href="substut1.html#V2" title="SUBSTUT1:attr.2">Sub_VERUM</a> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K10" title="QC_LANG1:func.10">@</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) &amp; ( <font color="Maroon" title="c1">S</font> is <a href="substut1.html#V4" title="SUBSTUT1:attr.4">Sub_atomic</a> implies  ex <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <span class="p1">(<span class="default"><a href="qc_lang1.html#K10" title="QC_LANG1:func.10">@</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 is   <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Olive" title="b1">k</font> ) &amp; ( <font color="Maroon" title="c1">S</font> is <a href="substut1.html#V5" title="SUBSTUT1:attr.5">Sub_negative</a> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K10" title="QC_LANG1:func.10">@</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) &amp; ( <font color="Maroon" title="c1">S</font> is <a href="substut1.html#V6" title="SUBSTUT1:attr.6">Sub_conjunctive</a> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K10" title="QC_LANG1:func.10">@</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 ) &amp; ( <font color="Maroon" title="c1">S</font> is <a href="substut1.html#V7" title="SUBSTUT1:attr.7">Sub_universal</a> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K10" title="QC_LANG1:func.10">@</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 ) )
 
<b>by </b><i><a class="ref" href="substut1.html#T25" target="_self" title="SUBSTUT1:th.25">Th25</a></i>;<br/>
<b>hence </b><a NAME="E2:73"/>
( not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">S</font> is <a href="substut1.html#V4" title="SUBSTUT1:attr.4">Sub_atomic</a> &amp; <font color="Maroon" title="c1">S</font> is <a href="substut1.html#V5" title="SUBSTUT1:attr.5">Sub_negative</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">S</font> is <a href="substut1.html#V4" title="SUBSTUT1:attr.4">Sub_atomic</a> &amp; <font color="Maroon" title="c1">S</font> is <a href="substut1.html#V6" title="SUBSTUT1:attr.6">Sub_conjunctive</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">S</font> is <a href="substut1.html#V4" title="SUBSTUT1:attr.4">Sub_atomic</a> &amp; <font color="Maroon" title="c1">S</font> is <a href="substut1.html#V7" title="SUBSTUT1:attr.7">Sub_universal</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">S</font> is <a href="substut1.html#V5" title="SUBSTUT1:attr.5">Sub_negative</a> &amp; <font color="Maroon" title="c1">S</font> is <a href="substut1.html#V6" title="SUBSTUT1:attr.6">Sub_conjunctive</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">S</font> is <a href="substut1.html#V5" title="SUBSTUT1:attr.5">Sub_negative</a> &amp; <font color="Maroon" title="c1">S</font> is <a href="substut1.html#V7" title="SUBSTUT1:attr.7">Sub_universal</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">S</font> is <a href="substut1.html#V6" title="SUBSTUT1:attr.6">Sub_conjunctive</a> &amp; <font color="Maroon" title="c1">S</font> is <a href="substut1.html#V7" title="SUBSTUT1:attr.7">Sub_universal</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">S</font> is <a href="substut1.html#V2" title="SUBSTUT1:attr.2">Sub_VERUM</a> &amp; <font color="Maroon" title="c1">S</font> is <a href="substut1.html#V4" title="SUBSTUT1:attr.4">Sub_atomic</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">S</font> is <a href="substut1.html#V2" title="SUBSTUT1:attr.2">Sub_VERUM</a> &amp; <font color="Maroon" title="c1">S</font> is <a href="substut1.html#V5" title="SUBSTUT1:attr.5">Sub_negative</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">S</font> is <a href="substut1.html#V2" title="SUBSTUT1:attr.2">Sub_VERUM</a> &amp; <font color="Maroon" title="c1">S</font> is <a href="substut1.html#V6" title="SUBSTUT1:attr.6">Sub_conjunctive</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">S</font> is <a href="substut1.html#V2" title="SUBSTUT1:attr.2">Sub_VERUM</a> &amp; <font color="Maroon" title="c1">S</font> is <a href="substut1.html#V7" title="SUBSTUT1:attr.7">Sub_universal</a> ) )
 <b>by </b><i><a class="ref" href="substut1.html#T26" target="_self" title="SUBSTUT1:th.26">Th26</a></i>;<br/>


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