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





<b>assume </b><b>that </b><br/><a NAME="E1:58"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">X</font> <a href="xboole_0.html#R2">c&lt;</a> <font color="Maroon">Y</font>
 <b>and </b><br/><a NAME="E2:58"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Z</font>
 ;<br/>

<a NAME="E3:58"/>
<font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T33" target="_self">Th33</a>, <a class="ref" href="xboole_0.html#D8">XBOOLE_0:def 8</a></i>;<br/>
<b>hence </b><a NAME="E4:58"/>
( <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Z</font> &amp; <font color="Maroon">X</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">Z</font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T33" target="_self">Th33</a>, <a class="ref" href="xboole_1.html#T34" target="_self">Th34</a>, , <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D8">XBOOLE_0:def 8</a><br/>


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