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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <a href="qc_lang1.html#K1">QC-variables</a> ;<br/>





<a NAME="E1:56"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="qc_lang2.html#K4">&lt;=&gt;</a> <font color="Maroon">c<sub>2</sub></font> is <a href="qc_lang2.html#V3">biconditional</a> &amp;  <a href="qc_lang2.html#K13">the_left_side_of</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="qc_lang2.html#K4">&lt;=&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="qc_lang2.html#K14">the_right_side_of</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="qc_lang2.html#K4">&lt;=&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="qc_lang2.html#T47">QC_LANG2:47</a>, <a class="ref" href="qc_lang2.html#D12">QC_LANG2:def 12</a></i>;<br/>
<b>hence </b><a NAME="E2:56"/>
 <a href="qc_lang3.html#K4" target="_self">Vars</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="qc_lang2.html#K4">&lt;=&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="qc_lang3.html#K4" target="_self">Vars</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="qc_lang3.html#K4" target="_self">Vars</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="qc_lang3.html#T60" target="_self">Th60</a></i>;<br/>


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