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<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font> be   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>;<br/><b>let </b><font color="Maroon" title="c3">H</font> be   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>;<br/>





<b>assume </b><a NAME="E1:68"/>
<font color="Maroon" title="c3">H</font> <a href="zf_lang.html#R1" title="ZF_LANG:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c1">x</font> <a href="zf_lang.html#K5" title="ZF_LANG:func.5">'in'</a> <font color="Maroon" title="c2">y</font>
 ;<br/>

<a NAME="E2:68"/><b>then </b><i><font color="Green" title="E54">A1</font></i>: 
( <font color="Maroon" title="c1">x</font> <a href="zf_lang.html#K5" title="ZF_LANG:func.5">'in'</a> <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c3">H</font> or  ex <font color="Olive" title="b1">H1</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a> st <br/>( <font color="Maroon" title="c1">x</font> <a href="zf_lang.html#K5" title="ZF_LANG:func.5">'in'</a> <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Olive" title="b1">H1</font> or <font color="Maroon" title="c1">x</font> <a href="zf_lang.html#K5" title="ZF_LANG:func.5">'in'</a> <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">H1</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c3">H</font> ) or  ex <font color="Olive" title="b1">z</font> being  <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a> st <font color="Maroon" title="c1">x</font> <a href="zf_lang.html#K5" title="ZF_LANG:func.5">'in'</a> <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Olive" title="b1">z</font>,<font color="Maroon" title="c3">H</font> )
 
<b>by </b><i><a class="ref" href="zf_lang.html#D39" target="_self" title="ZF_LANG:def.39">Def39</a></i>;<br/>
<a NAME="E3:68"/><i><font color="Green" title="E55">A2</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="zf_lang.html#K5" title="ZF_LANG:func.5">'in'</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <span class="p1">(<span class="default"><a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c3">H</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 )
 
<b>by </b><i><a class="ref" href="zf_lang.html#T31" target="_self" title="ZF_LANG:th.31">Th31</a>, <a class="ref" href="finseq_1.html#T58" title="FINSEQ_1:th.58">FINSEQ_1:58</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c4">z</font> being   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a><b> such that </b><br/><a NAME="E5:68"/><i><font color="Green" title="E56">A3</font></i>: 
<font color="Maroon" title="c1">x</font> <a href="zf_lang.html#K5" title="ZF_LANG:func.5">'in'</a> <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c3">H</font>
 <b>by </b><i><a class="txt" href="zf_lang.html#E2:68"><i><font color="Green" title="E54">A1</font></i></a>, <a class="ref" href="zf_lang.html#T33" target="_self" title="ZF_LANG:th.33">Th33</a></i>;<br/>
<b>thus </b><a NAME="E6:68"/>
contradiction
 <b>by </b><i><a class="txt" href="zf_lang.html#E3:68"><i><font color="Green" title="E55">A2</font></i></a>, <a class="txt" href="zf_lang.html#E5:68"><i><font color="Green" title="E56">A3</font></i></a>, <a class="ref" href="zf_lang.html#T34" target="_self" title="ZF_LANG:th.34">Th34</a></i>;<br/>


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