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

<b>assume </b><a NAME="E1:36"/>
not  <a href="modal_1.html#K4" title="MODAL_1:func.4">MP-conectives</a>  <a href="subset_1.html#R1" title="SUBSET_1:pred.1">misses</a>  <a href="modal_1.html#K3" title="MODAL_1:func.3">MP-variables</a> 
 ;<br/>

<b>then consider </b><font color="Maroon" title="c1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:36"/><i><font color="Green" title="E29">A1</font></i>: 
( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="mcart_1.html#K12" title="MCART_1:func.12">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default">0,1,2</span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span>,<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span> &amp; <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="mcart_1.html#K12" title="MCART_1:func.12">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">3</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span> )
 <b>by </b><i><a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c2">x1</font>, <font color="Maroon" title="c3">x2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E5:36"/><i><font color="Green" title="E30">A2</font></i>: 
( <font color="Maroon" title="c2">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default">0,1,2</span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> &amp; <font color="Maroon" title="c3">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  &amp; <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">x2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )
 <b>by </b><i><a class="txt" href="modal_1.html#E3:36"><i><font color="Green" title="E29">A1</font></i></a>, <a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></i>;<br/>
<a NAME="E6:36"/>
<font color="Maroon" title="c2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 
<b>by </b><i><a class="txt" href="modal_1.html#E3:36"><i><font color="Green" title="E29">A1</font></i></a>, <a class="txt" href="modal_1.html#E5:36"><i><font color="Green" title="E30">A2</font></i></a>, <a class="ref" href="zfmisc_1.html#T128" title="ZFMISC_1:th.128">ZFMISC_1:128</a></i>;<br/>
<b>hence </b><a NAME="E7:36"/>
contradiction
 <b>by </b><i><a class="txt" href="modal_1.html#E5:36"><i><font color="Green" title="E30">A2</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/>


</div>
