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





<b>assume </b><a NAME="E1:21_1_3"/><i><font color="Green">E22</font></i>: 
for <font color="Olive">Z</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">Z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">SFZ</font> iff  ex <font color="Olive">X</font>, <font color="Olive">Y</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">X</font> <a href="hidden.html#R2">in</a> <font color="Maroon">SFX</font> &amp; <font color="Olive">Y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">SFY</font> &amp; <font color="Olive">Z</font> <a href="hidden.html#R1">=</a> <font color="Olive">X</font> <a href="xboole_0.html#K2">\/</a> <font color="Olive">Y</font> ) )
 ;<br/>

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

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:21_1_3_1"/>
<font color="Maroon">Z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">SFZ</font>
 ;<br/><a NAME="E2:21_1_3_1"/><b>then </b>
 ex <font color="Olive">X</font>, <font color="Olive">Y</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">X</font> <a href="hidden.html#R2">in</a> <font color="Maroon">SFX</font> &amp; <font color="Olive">Y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">SFY</font> &amp; <font color="Maroon">Z</font> <a href="hidden.html#R1">=</a> <font color="Olive">X</font> <a href="xboole_0.html#K2">\/</a> <font color="Olive">Y</font> )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:21_1_3_1"/>
 ex <font color="Olive">Y</font>, <font color="Olive">X</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">Y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">SFY</font> &amp; <font color="Olive">X</font> <a href="hidden.html#R2">in</a> <font color="Maroon">SFX</font> &amp; <font color="Maroon">Z</font> <a href="hidden.html#R1">=</a> <font color="Olive">Y</font> <a href="xboole_0.html#K2">\/</a> <font color="Olive">X</font> )
 ;<br/></div>
<b>end;</b></div>

<b>thus </b><a NAME="E3:21_1_3"/>
(  ex <font color="Olive">X</font>, <font color="Olive">Y</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">X</font> <a href="hidden.html#R2">in</a> <font color="Maroon">SFY</font> &amp; <font color="Olive">Y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">SFX</font> &amp; <font color="Maroon">Z</font> <a href="hidden.html#R1">=</a> <font color="Olive">X</font> <a href="xboole_0.html#K2">\/</a> <font color="Olive">Y</font> ) implies <font color="Maroon">Z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">SFZ</font> )
 <b>by </b><i/>;<br/>


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