<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="zf_lang.html#NM1">Variable</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="zf_lang.html#NM2">ZF-formula</a>;<br/>





<b>assume </b><a NAME="E1:68"/>
<font color="Maroon">c<sub>3</sub></font> <a href="zf_lang.html#R1" target="_self">is_immediate_constituent_of</a> <font color="Maroon">c<sub>1</sub></font> <a href="zf_lang.html#K5" target="_self">'in'</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:68"/><b>then </b><i><font color="Green">E56</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="zf_lang.html#K5" target="_self">'in'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="zf_lang.html#K6" target="_self">'not'</a> <font color="Maroon">c<sub>3</sub></font> or ex <font color="Olive">b<sub>1</sub></font> being  <a href="zf_lang.html#NM2">ZF-formula</a> st <br/>( <font color="Maroon">c<sub>1</sub></font> <a href="zf_lang.html#K5" target="_self">'in'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="zf_lang.html#K7" target="_self">'&amp;'</a> <font color="Olive">b<sub>1</sub></font> or <font color="Maroon">c<sub>1</sub></font> <a href="zf_lang.html#K5" target="_self">'in'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="zf_lang.html#K7" target="_self">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font> ) or ex <font color="Olive">b<sub>1</sub></font> being  <a href="zf_lang.html#NM1">Variable</a> st <font color="Maroon">c<sub>1</sub></font> <a href="zf_lang.html#K5" target="_self">'in'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="zf_lang.html#K8" target="_self">All</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="zf_lang.html#D39" target="_self">Def39</a></i>;<br/>
<a NAME="E3:68"/><i><font color="Green">E57</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="zf_lang.html#K5" target="_self">'in'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 1 &amp; <span class="p1">(<span class="default"><a href="zf_lang.html#K6" target="_self">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 2 )
 
<b>by </b><i><a class="ref" href="zf_lang.html#T31" target="_self">Th31</a>, <a class="ref" href="zf_lang.html#T32" target="_self">Th32</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="zf_lang.html#NM1">Variable</a><b> such that </b><br/><a NAME="E5:68"/><i><font color="Green">E58</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="zf_lang.html#K5" target="_self">'in'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="zf_lang.html#K8" target="_self">All</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="zf_lang.html#E2:68"><i><font color="Green">E56</font></i></a>, <a class="ref" href="zf_lang.html#T33" target="_self">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">E57</font></i></a>, <a class="txt" href="zf_lang.html#E5:68"><i><font color="Green">E58</font></i></a>, <a class="ref" href="zf_lang.html#T34" target="_self">Th34</a></i>;<br/>


</div>
