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<span class="kw">assume </span><a NAME="E1:142_1_1"/>
 not <font color="Maroon" title="c1">A</font> <a href="member_1.html#K13" title="MEMBER_1:func.13">**</a> <font color="Maroon" title="c2">B</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:142_1_1"/><span class="kw">then </span>
 the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">A</font> <a href="member_1.html#K13" title="MEMBER_1:func.13">**</a> <font color="Maroon" title="c2">B</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">A</font> <a href="member_1.html#K13" title="MEMBER_1:func.13">**</a> <font color="Maroon" title="c2">B</font>
 
;<br/>
<a NAME="E3:142_1_1"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">c1</font>, <font color="Olive" title="b2">c2</font> being   <a href="xcmplx_0.html#NM1" title="XCMPLX_0:NM.1">Complex</a> st <br/>(  the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">A</font> <a href="member_1.html#K13" title="MEMBER_1:func.13">**</a> <font color="Maroon" title="c2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">c1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b2">c2</font> &amp; <font color="Olive" title="b1">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> &amp; <font color="Olive" title="b2">c2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">B</font> )
 
;<br/>
<span class="kw">hence </span><a NAME="E4:142_1_1"/>
contradiction
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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