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<b>let </b><font color="Maroon">A</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">x</font> be   <a href="qc_lang1.html#NM3">bound_QC-variable</a>;<br/><b>let </b><font color="Maroon">p</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/><b>let </b><font color="Maroon">q</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/><b>let </b><font color="Maroon">J</font> be    <a href="valuat_1.html#M1" target="_self">interpretation</a> of <font color="Maroon">A</font>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:61"/><i><font color="Green">E25</font></i>: 
for <font color="Olive">v</font> being   <a href="fraenkel.html#M2">Element</a> of  <a href="valuat_1.html#K2" target="_self">Valuations_in</a> <font color="Maroon">A</font> holds  <font color="Maroon">J</font>,<font color="Olive">v</font> <a href="valuat_1.html#R1" target="_self">|=</a> <font color="Maroon">p</font> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">q</font>
 <b>and </b><br/><a NAME="E2:61"/><i><font color="Green">E30</font></i>: 
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K23">still_not-bound_in</a> <font color="Maroon">p</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="valuat_1.html#D13" target="_self">VALUAT_1:def 13</a><br/>

<b>let </b><font color="Maroon">u</font> be    <a href="fraenkel.html#M2">Element</a> of  <a href="valuat_1.html#K2" target="_self">Valuations_in</a> <font color="Maroon">A</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="valuat_1.html#D13" target="_self">VALUAT_1:def 13</a><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:61_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">J</font>,<font color="Maroon">u</font> <a href="valuat_1.html#R1" target="_self">|=</a> <font color="Maroon">p</font>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">w</font> be    <a href="fraenkel.html#M2">Element</a> of  <a href="valuat_1.html#K2" target="_self">Valuations_in</a> <font color="Maroon">A</font>;<br/><b>assume </b><a NAME="E1:61_1_1"/>
for <font color="Olive">y</font> being  <a href="qc_lang1.html#NM3">bound_QC-variable</a>  st <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">y</font> holds <br/><font color="Maroon">w</font> <a href="funct_2.html#K3">.</a> <font color="Olive">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">u</font> <a href="funct_2.html#K3">.</a> <font color="Olive">y</font>
 ;<br/><a NAME="E2:61_1_1"/><b>then </b><i><font color="Green">E33</font></i>: 
<font color="Maroon">J</font>,<font color="Maroon">w</font> <a href="valuat_1.html#R1" target="_self">|=</a> <font color="Maroon">p</font>
 <b>by </b><i>, , <a class="txt" href="valuat_1.html#E2:61"><i><font color="Green">E30</font></i></a></i>;<br/><a NAME="E3:61_1_1"/>
<font color="Maroon">J</font>,<font color="Maroon">w</font> <a href="valuat_1.html#R1" target="_self">|=</a> <font color="Maroon">p</font> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">q</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E4:61_1_1"/>
<font color="Maroon">J</font>,<font color="Maroon">w</font> <a href="valuat_1.html#R1" target="_self">|=</a> <font color="Maroon">q</font>
 <b>by </b><i><a class="ref" href="valuat_1.html#D4" target="_self">Def4</a>, <a class="txt" href="valuat_1.html#E1:61"><i><font color="Green">E25</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:61_1"/>
<font color="Maroon">J</font>,<font color="Maroon">u</font> <a href="valuat_1.html#R1" target="_self">|=</a>  <a href="cqc_lang.html#K15">All</a> <font color="Maroon">x</font>,<font color="Maroon">q</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:61"/>
<font color="Maroon">J</font>,<font color="Maroon">u</font> <a href="valuat_1.html#R1" target="_self">|=</a> <font color="Maroon">p</font> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">x</font>,<font color="Maroon">q</font></span>)</span>
 <b>by </b><i><a class="txt" href="valuat_1.html#E1:61"><i><font color="Green">E25</font></i></a></i>;<br/>


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