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

<b>assume </b><b>that </b><br/><a NAME="E1:4"/><i><font color="Green">E5</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">b</font>
 <b>and </b><br/><a NAME="E2:4"/><i><font color="Green">E8</font></i>: 
<font color="Maroon">b</font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">c</font>
 ;<br/>

<a NAME="E3:4"/>
<font color="Maroon">b</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c</font>
 
<b>by </b><i>, <a class="ref" href="subset.html#T1" target="_self">Th1</a></i>;<br/>
<a NAME="E4:4"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">c</font>
 
<b>by </b><i>, <a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<a NAME="E5:4"/><b>then </b>
<font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/>
<b>hence </b><a NAME="E6:4"/>
not <font color="Maroon">c</font> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i><a class="ref" href="xboole_0.html#D5">XBOOLE_0:def 5</a></i>;<br/>


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