<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">G</font>, <font color="Maroon" title="c2">H</font> be   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</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="c1">G</font> <a href="zf_lang.html#R3" title="ZF_LANG:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c2">H</font> or  not <font color="Maroon" title="c2">H</font> <a href="zf_lang.html#R3" title="ZF_LANG:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c1">G</font> )</span><br/>



<b>assume </b><a NAME="E1:33"/>
( <font color="Maroon" title="c1">G</font> <a href="zf_lang.html#R3" title="ZF_LANG:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c2">H</font> &amp; <font color="Maroon" title="c2">H</font> <a href="zf_lang.html#R3" title="ZF_LANG:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c1">G</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:33"/><b>then </b>
<font color="Maroon" title="c1">G</font> <a href="zf_lang.html#R3" title="ZF_LANG:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c1">G</font>
 
<b>by </b><i><a class="ref" href="zf_lang.html#T85" title="ZF_LANG:th.85">ZF_LANG:85</a></i>;<br/>
<b>hence </b><a NAME="E3:33"/>
contradiction
 <b>by </b><i><a class="ref" href="zf_lang.html#D41" title="ZF_LANG:def.41">ZF_LANG:def 41</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
