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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><a NAME="E1:6"/><i><font color="Green">E13</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( not <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> iff ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> iff <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> ) )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><a NAME="E1:6_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> iff ( ( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> &amp; not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> &amp; not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> ) ) )
 <b>by </b><i/>;<br/><a NAME="E2:6_1"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> iff ( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> <a href="xboole_0.html#K4" target="_self">\</a> <font color="Maroon">Z</font> or <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> <a href="xboole_0.html#K4" target="_self">\</a> <font color="Maroon">Y</font> ) )
 <b>by </b><i/>;<br/><a NAME="E3:6_1"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> iff <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">Y</font> <a href="xboole_0.html#K4" target="_self">\</a> <font color="Maroon">Z</font></span>)</span> <a href="xboole_0.html#K2" target="_self">\/</a> <span class="p1">(<span class="default"><font color="Maroon">Z</font> <a href="xboole_0.html#K4" target="_self">\</a> <font color="Maroon">Y</font></span>)</span> )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E4:6_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> iff <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> <a href="xboole_0.html#K5" target="_self">\+\</a> <font color="Maroon">Z</font> )
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:6"/>
<font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Y</font> <a href="xboole_0.html#K5" target="_self">\+\</a> <font color="Maroon">Z</font>
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>


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