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<b>let </b><font color="Maroon" title="c1">H</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qc_lang1.html#K8" title="QC_LANG1:func.8">QC-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">H</font> is <a href="qc_lang2.html#V3" title="QC_LANG2:attr.3">biconditional</a> implies ( <font color="Maroon" title="c1">H</font> is <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a> &amp;  <a href="qc_lang1.html#K18" title="QC_LANG1:func.18">the_left_argument_of</a> <font color="Maroon" title="c1">H</font> is <a href="qc_lang2.html#V2" title="QC_LANG2:attr.2">conditional</a> &amp;  <a href="qc_lang1.html#K19" title="QC_LANG1:func.19">the_right_argument_of</a> <font color="Maroon" title="c1">H</font> is <a href="qc_lang2.html#V2" title="QC_LANG2:attr.2">conditional</a> ) )</span><br/>

<b>given </b><font color="Maroon" title="c2">F</font>, <font color="Maroon" title="c3">G</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qc_lang1.html#K8" title="QC_LANG1:func.8">QC-WFF</a> <b> such that </b><a NAME="E2:32"/><i><font color="Green" title="E17">A1</font></i>: 
<font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">F</font> <a href="qc_lang2.html#K4" title="QC_LANG2:func.4">&lt;=&gt;</a> <font color="Maroon" title="c3">G</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="qc_lang2.html#D12" target="_self" title="QC_LANG2:def.12">QC_LANG2:def 12</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">H</font> is <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a> &amp;  <a href="qc_lang1.html#K18" title="QC_LANG1:func.18">the_left_argument_of</a> <font color="Maroon" title="c1">H</font> is <a href="qc_lang2.html#V2" title="QC_LANG2:attr.2">conditional</a> &amp;  <a href="qc_lang1.html#K19" title="QC_LANG1:func.19">the_right_argument_of</a> <font color="Maroon" title="c1">H</font> is <a href="qc_lang2.html#V2" title="QC_LANG2:attr.2">conditional</a> )</span><br/>

<a NAME="E3:32"/>
( <font color="Maroon" title="c1">H</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="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <font color="Maroon" title="c3">G</font></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="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <font color="Maroon" title="c2">F</font></span>)</span> &amp;  <a href="qc_lang1.html#K18" title="QC_LANG1:func.18">the_left_argument_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <font color="Maroon" title="c3">G</font></span>)</span> <a href="qc_lang1.html#K13" title="QC_LANG1:func.13">'&amp;'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <font color="Maroon" title="c2">F</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">F</font> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <font color="Maroon" title="c3">G</font> &amp;  <a href="qc_lang1.html#K19" title="QC_LANG1:func.19">the_right_argument_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <font color="Maroon" title="c3">G</font></span>)</span> <a href="qc_lang1.html#K13" title="QC_LANG1:func.13">'&amp;'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <font color="Maroon" title="c2">F</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">G</font> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <font color="Maroon" title="c2">F</font> )
 
<b>by </b><i><a class="txt" href="#E2:32"><i><font color="Green" title="E17">A1</font></i></a>, <a class="ref" href="qc_lang2.html#T5" target="_self" title="QC_LANG2:th.5">Th5</a></i>;<br/>
<b>hence </b><a NAME="E4:32"/>
( <font color="Maroon" title="c1">H</font> is <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a> &amp;  <a href="qc_lang1.html#K18" title="QC_LANG1:func.18">the_left_argument_of</a> <font color="Maroon" title="c1">H</font> is <a href="qc_lang2.html#V2" title="QC_LANG2:attr.2">conditional</a> &amp;  <a href="qc_lang1.html#K19" title="QC_LANG1:func.19">the_right_argument_of</a> <font color="Maroon" title="c1">H</font> is <a href="qc_lang2.html#V2" title="QC_LANG2:attr.2">conditional</a> )
 <b>by </b><i><a class="ref" href="qc_lang2.html#D11" target="_self" title="QC_LANG2:def.11">Def11</a>, <a class="ref" href="qc_lang1.html#D19" title="QC_LANG1:def.19">QC_LANG1:def 19</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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