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<div class="add">

<div><b>hereby </b>
<div class="add"><b>consider </b><font color="Maroon" title="c1">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="funct_5.html#K1" title="FUNCT_5:func.1">proj1</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ;<br/><b>assume </b><a NAME="E2:9_1"/>
 <a href="funct_5.html#K1" title="FUNCT_5:func.1">proj1</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><a NAME="E3:9_1"/><b>then </b>
 ex <font color="Olive" title="b1">y</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Olive" title="b1">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="ref" href="funct_5.html#D1" target="_self" title="FUNCT_5:def.1">Def1</a></i>;<br/><b>hence </b><a NAME="E4:9_1"/>
contradiction
 ;<br/></div>
<b>end;</b></div>

<b>consider </b><font color="Maroon" title="c1">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="funct_5.html#K2" title="FUNCT_5:func.2">proj2</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ;<br/>
<b>assume </b><a NAME="E3:9"/>
 <a href="funct_5.html#K2" title="FUNCT_5:func.2">proj2</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/>

<a NAME="E4:9"/><b>then </b>
 ex <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">x</font>,<font color="Maroon" title="c1">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="funct_5.html#D2" target="_self" title="FUNCT_5:def.2">Def2</a></i>;<br/>
<b>hence </b><a NAME="E5:9"/>
contradiction
 ;<br/>


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