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<span class="kw">let </span><font color="Maroon" title="c1">p</font> be   <a href="qc_lang1.html#NM8" title="QC_LANG1:NM.8">QC-formula</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">p</font> is  <a href="qc_lang2.html#V2" title="QC_LANG2:attr.2">conditional</a>  implies  <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><a href="qc_lang2.html#K12" title="QC_LANG2:func.12">the_antecedent_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><a href="qc_lang2.html#NK13" title="QC_LANG2:NK.13">the_consequent_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">p1</font> =  <a href="qc_lang2.html#K12" title="QC_LANG2:func.12">the_antecedent_of</a> <font color="Maroon" title="c1">p</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c3">p2</font> =  <a href="qc_lang2.html#NK13" title="QC_LANG2:NK.13">the_consequent_of</a> <font color="Maroon" title="c1">p</font>;<br/>
<span class="kw">assume </span><a NAME="E1:22"/>
<font color="Maroon" title="c1">p</font> is  <a href="qc_lang2.html#V2" title="QC_LANG2:attr.2">conditional</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><a href="qc_lang2.html#K12" title="QC_LANG2:func.12">the_antecedent_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><a href="qc_lang2.html#NK13" title="QC_LANG2:NK.13">the_consequent_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span></span><br/>

<a NAME="E2:22"/><span class="kw">then </span>
<font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="qc_lang2.html#K12" title="QC_LANG2:func.12">the_antecedent_of</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <span class="p1">(<span class="default"><a href="qc_lang2.html#NK13" title="QC_LANG2:NK.13">the_consequent_of</a> <font color="Maroon" title="c1">p</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang2.html#T38" title="QC_LANG2:th.38">QC_LANG2:38</a></span>;<br/>
<a NAME="E3:22"/><span class="kw">then </span>
<font color="Maroon" title="c1">p</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"><span class="p2">(<span class="default"><a href="qc_lang2.html#K12" title="QC_LANG2:func.12">the_antecedent_of</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="qc_lang1.html#K13" title="QC_LANG1:func.13">'&amp;'</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <span class="p3">(<span class="default"><a href="qc_lang2.html#NK13" title="QC_LANG2:NK.13">the_consequent_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang2.html#D2" title="QC_LANG2:def.2">QC_LANG2:def 2</a></span>;<br/>
<span class="kw">then </span> <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font> = 
 <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang2.html#K12" title="QC_LANG2:func.12">the_antecedent_of</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="qc_lang1.html#K13" title="QC_LANG1:func.13">'&amp;'</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <span class="p3">(<span class="default"><a href="qc_lang2.html#NK13" title="QC_LANG2:NK.13">the_consequent_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang3.html#T7" target="_self" title="QC_LANG3:th.7">Th11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><a href="qc_lang2.html#K12" title="QC_LANG2:func.12">the_antecedent_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <span class="p3">(<span class="default"><a href="qc_lang2.html#NK13" title="QC_LANG2:NK.13">the_consequent_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang3.html#T10" target="_self" title="QC_LANG3:th.10">Th14</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><a href="qc_lang2.html#K12" title="QC_LANG2:func.12">the_antecedent_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><a href="qc_lang2.html#NK13" title="QC_LANG2:NK.13">the_consequent_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang3.html#T7" target="_self" title="QC_LANG3:th.7">Th11</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E5:22"/>
 <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><a href="qc_lang2.html#K12" title="QC_LANG2:func.12">the_antecedent_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><a href="qc_lang2.html#NK13" title="QC_LANG2:NK.13">the_consequent_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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