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<b>let </b><font color="Maroon" title="c1">x</font> be   <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">S</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="substut1.html#K38" title="SUBSTUT1:func.38">CQC-Sub-WFF</a>   st <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <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> holds <br/><span class="p1">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <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> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> is   <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a></span><br/><b>let </b><font color="Maroon" title="c2">S</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="substut1.html#K38" title="SUBSTUT1:func.38">CQC-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">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a> </span>)</span></span>)</span> implies <span class="p1">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> is   <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a> )</span><br/>



<b>assume </b><a NAME="E1:49"/>
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a> </span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> is   <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a></span><br/>

<a NAME="E2:49"/><b>then </b>
<span class="p1">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_1.html#T12" title="FUNCT_1:th.12">FUNCT_1:12</a></i>;<br/>
<b>hence </b><a NAME="E3:49"/>
<span class="p1">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> is   <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a>
 ; <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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