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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="qc_lang1.html#NM3">bound_QC-variable</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="fraenkel.html#M2">Element</a> of  <a href="valuat_1.html#K2">Valuations_in</a> <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="subset_1.html#M2">Element</a> of  <a href="substut1.html#K38">CQC-Sub-WFF</a> ;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="substut1.html#M1">second_Q_comp</a> of <span class="p1"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="sublemma.html#K8" target="_self">]</a></span>;<br/>









<a NAME="E1:88"/>
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="substut1.html#K2">@</a> <span class="p2">(<span class="default"><a href="substut1.html#K7">RestrictSub</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="qc_lang1.html#K2">bound_QC-variables</a> 
 
;<br/>
<a NAME="E2:88"/><b>then </b><i><font color="Green">E70</font></i>: 
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="substut1.html#K2">@</a> <span class="p2">(<span class="default"><a href="substut1.html#K7">RestrictSub</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="sublemma.html#T59" target="_self">Th59</a></i>;<br/>
<a NAME="E3:88"/>
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="substut1.html#K2">@</a> <span class="p2">(<span class="default"><a href="substut1.html#K7">RestrictSub</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="sublemma.html#E2:88"><i><font color="Green">E70</font></i></a>, <a class="ref" href="relat_1.html#T46">RELAT_1:46</a></i>;<br/>
<b>hence </b><a NAME="E4:88"/>
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="substut1.html#K7">RestrictSub</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span>,<font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="substut1.html#D2">SUBSTUT1:def 2</a></i>;<br/>


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