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

<a NAME="E1:28"/><i><font color="Green">E20</font></i>: 
1 <a href="hidden.html#R1">=</a>  <a href="ordinal1.html#K1">succ</a> 0
 
;<br/>
<a NAME="E2:28"/><i><font color="Green">E21</font></i>: 
 <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">c<sub>1</sub></font>,<a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="txt" href="classes1.html#E15"><i><font color="Green">Lemma10</font></i></a></i>;<br/>
<a NAME="E3:28"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">c<sub>1</sub></font>,<a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E4:28"/><b>then </b><i><font color="Green">E22</font></i>: 
 <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="classes1.html#T7" target="_self">Th7</a></i>;<br/>
<a NAME="E5:28"/>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">c<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:28_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span>
 ;<br/>

<a NAME="E2:28_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:28_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#D1">ZFMISC_1:def 1</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E6:28"/><b>then </b>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="classes1.html#E4:28"><i><font color="Green">E22</font></i></a>, <a class="ref" href="classes1.html#T6" target="_self">Th6</a></i>;<br/>
<b>hence </b><a NAME="E7:28"/><i><font color="Green">E23</font></i>: 
 <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">c<sub>1</sub></font>,<a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">c<sub>1</sub></font>,1
 <b>by </b><i><a class="txt" href="classes1.html#E2:28"><i><font color="Green">E21</font></i></a>, <a class="ref" href="classes1.html#T13" target="_self">Th13</a>, <a class="txt" href="classes1.html#E1:28"><i><font color="Green">E20</font></i></a></i>;<br/>

<b>assume </b><a NAME="E8:28"/>
 <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">c<sub>1</sub></font>,<a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R1">=</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">c<sub>1</sub></font>,1
 ;<br/>

<b>hence </b><a NAME="E9:28"/>
contradiction
 <b>by </b><i><a class="txt" href="classes1.html#E7:28"><i><font color="Green">E23</font></i></a></i>;<br/>


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