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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="E1:13_1_1"/><i><font color="Green">E3</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being <a href="facirc_1.html#V1" target="_self">pair</a>  <a href="hidden.html#M1">set</a>  holds not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="facirc_1.html#D2" target="_self">FACIRC_1:def 2</a><br/>

<b>assume </b><a NAME="E2:13_1_1"/><i><font color="Green">E4</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> holds <br/>ex <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font></span><a href="tarski.html#K4">]</a></span>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="relat_1.html#D1">RELAT_1:def 1</a><br/>

<b>assume </b><a NAME="E3:13_1_1"/>
not <font color="Maroon">c<sub>1</sub></font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>2</sub></font> = <font color="Maroon">c<sub>1</sub></font> as  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a>  ;<br/>
<b>consider </b><font color="Maroon">c<sub>3</sub></font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>
<a NAME="E6:13_1_1"/>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <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>
 
<b>by </b><i><a class="txt" href="facirc_1.html#E2:13_1_1"><i><font color="Green">E4</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:13_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="facirc_1.html#E1:13_1_1"><i><font color="Green">E3</font></i></a></i>;<br/>


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