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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:15"/><i><font color="Green">E13</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="hidden.html#M1">set</a>  holds not <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<div><b>hereby </b>
<div class="add"><b>consider </b><font color="Maroon">c<sub>2</sub></font> being    <a href="subset_1.html#M1">Element</a> of  <a href="funct_5.html#K1" target="_self">proj1</a> <font color="Maroon">c<sub>1</sub></font>;<br/><b>assume </b><a NAME="E2:15_1"/>
 <a href="funct_5.html#K1" target="_self">proj1</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><a NAME="E3:15_1"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="funct_5.html#D1" target="_self">Def1</a></i>;<br/><b>hence </b><a NAME="E4:15_1"/>
contradiction
 <b>by </b><i><a class="txt" href="funct_5.html#E1:15"><i><font color="Green">E13</font></i></a></i>;<br/></div>
<b>end;</b></div>

<b>consider </b><font color="Maroon">c<sub>2</sub></font> being    <a href="subset_1.html#M1">Element</a> of  <a href="funct_5.html#K2" target="_self">proj2</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>assume </b><a NAME="E4:15"/>
 <a href="funct_5.html#K2" target="_self">proj2</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<a NAME="E5:15"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="funct_5.html#D2" target="_self">Def2</a></i>;<br/>
<b>hence </b><a NAME="E6:15"/>
contradiction
 <b>by </b><i><a class="txt" href="funct_5.html#E1:15"><i><font color="Green">E13</font></i></a></i>;<br/>


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