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<b>assume </b><a NAME="E1:15_1_1"/>
not  <a href="member_1.html#K1" title="MEMBER_1:func.1">--</a> <font color="Maroon" title="c1">F</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:15_1_1"/><b>then </b>
the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="member_1.html#K1" title="MEMBER_1:func.1">--</a> <font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="member_1.html#K1" title="MEMBER_1:func.1">--</a> <font color="Maroon" title="c1">F</font>
 
;<br/>
<a NAME="E3:15_1_1"/><b>then </b>
 ex <font color="Olive" title="b1">w</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K7" title="NUMBERS:func.7">ExtREAL</a>  st <br/>( the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="member_1.html#K1" title="MEMBER_1:func.1">--</a> <font color="Maroon" title="c1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <font color="Olive" title="b1">w</font> &amp; <font color="Olive" title="b1">w</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">F</font> )
 
;<br/>
<b>hence </b><a NAME="E4:15_1_1"/>
contradiction
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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