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<span class="kw">assume </span><a NAME="E1:186_1_1"/>
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">f</font>
 ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="setfam_1.html#D9" title="SETFAM_1:def.9">SETFAM_1:def 9</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:186_1_1"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">f</font> &amp;  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D5" target="_self" title="FUNCT_1:def.5">Def5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:186_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D15" target="_self" title="FUNCT_1:def.15">Def15</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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