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<b>assume </b><a NAME="E1:21_1"/>
<span class="p1">{<span class="default"> <font color="Maroon">F<sub>3</sub></font>(<font color="Olive">b<sub>1</sub></font>) where B is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() : ( <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] &amp; not <font color="Maroon">F<sub>3</sub></font>(<font color="Olive">b<sub>1</sub></font>) <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>() ) </span>}</span>  <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">F<sub>2</sub></font>()
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>1</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:21_1"/><i><font color="Green">E4</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Maroon">F<sub>3</sub></font>(<font color="Olive">b<sub>1</sub></font>) where B is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() : ( <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] &amp; not <font color="Maroon">F<sub>3</sub></font>(<font color="Olive">b<sub>1</sub></font>) <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>() ) </span>}</span>  &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>() )
 <b>by </b><i><a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/>
<a NAME="E4:21_1"/>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() st <br/>( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>3</sub></font>(<font color="Olive">b<sub>1</sub></font>) &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] &amp; not <font color="Maroon">F<sub>3</sub></font>(<font color="Olive">b<sub>1</sub></font>) <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>() )
 
<b>by </b><i><a class="txt" href="fraenkel.html#E3:21_1"><i><font color="Green">E4</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:21_1"/>
contradiction
 <b>by </b><i><a class="txt" href="fraenkel.html#E3:21_1"><i><font color="Green">E4</font></i></a></i>;<br/>


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