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<b>let </b><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">X</font> is <a href="valued_2.html#V1" title="VALUED_2:attr.1">complex-functions-membered</a> implies <font color="Maroon" title="c1">X</font> is <a href="fraenkel.html#V1" title="FRAENKEL:attr.1">functional</a> )</span><br/>

<b>assume </b><a NAME="E1:11_1_1"/><i><font color="Green" title="E8">A1</font></i>: 
<font color="Maroon" title="c1">X</font> is <a href="valued_2.html#V1" title="VALUED_2:attr.1">complex-functions-membered</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">X</font> is <a href="fraenkel.html#V1" title="FRAENKEL:attr.1">functional</a></span><br/>

<b>let </b><font color="Maroon" title="c2">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="fraenkel.html#D1" title="FRAENKEL:def.1">FRAENKEL:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> or <font color="Maroon" title="c2">x</font> is    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  )</span><br/>

<b>thus </b><a NAME="E2:11_1_1"/>
(  not <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> or <font color="Maroon" title="c2">x</font> is    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  )
 <b>by </b><i><a class="txt" href="#E1:11_1_1"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="valued_2.html#D1" target="_self" title="VALUED_2:def.1">Def1</a></i>; <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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