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

<b>let </b><font color="Maroon">H</font> be   <a href="zf_lang.html#NM2">ZF-formula</a>;<br/><b>let </b><font color="Maroon">G</font> be   <a href="zf_lang.html#NM2">ZF-formula</a>;<br/><b>let </b><font color="Maroon">F</font> be   <a href="zf_lang.html#NM2">ZF-formula</a>;<br/>





<b>assume </b><a NAME="E1:109"/><i><font color="Green">E31</font></i>: 
( ( <font color="Maroon">H</font> <a href="zf_lang.html#R1" target="_self">is_immediate_constituent_of</a> <font color="Maroon">G</font> or <font color="Maroon">H</font> <a href="zf_lang.html#R3" target="_self">is_proper_subformula_of</a> <font color="Maroon">G</font> or <font color="Maroon">H</font> <a href="zf_lang.html#R2" target="_self">is_subformula_of</a> <font color="Maroon">G</font> ) &amp; <font color="Maroon">G</font> <a href="hidden.html#R2">in</a>  <a href="zf_lang.html#K29" target="_self">Subformulae</a> <font color="Maroon">F</font> )
 ;<br/>

<a NAME="E2:109"/><b>then </b>
( <font color="Maroon">H</font> <a href="zf_lang.html#R3" target="_self">is_proper_subformula_of</a> <font color="Maroon">G</font> or <font color="Maroon">H</font> <a href="zf_lang.html#R2" target="_self">is_subformula_of</a> <font color="Maroon">G</font> )
 
<b>by </b><i><a class="ref" href="zf_lang.html#D20" target="_self">Def20</a></i>;<br/>
<a NAME="E3:109"/><b>then </b>
( <font color="Maroon">H</font> <a href="zf_lang.html#R2" target="_self">is_subformula_of</a> <font color="Maroon">G</font> &amp; <font color="Maroon">G</font> <a href="zf_lang.html#R2" target="_self">is_subformula_of</a> <font color="Maroon">F</font> )
 
<b>by </b><i>, <a class="ref" href="zf_lang.html#D14" target="_self">Def14</a>, <a class="ref" href="zf_lang.html#T35" target="_self">Th35</a></i>;<br/>
<a NAME="E4:109"/><b>then </b>
<font color="Maroon">H</font> <a href="zf_lang.html#R2" target="_self">is_subformula_of</a> <font color="Maroon">F</font>
 
<b>by </b><i><a class="ref" href="zf_lang.html#T25" target="_self">Th25</a></i>;<br/>
<b>hence </b><a NAME="E5:109"/>
<font color="Maroon">H</font> <a href="hidden.html#R2">in</a>  <a href="zf_lang.html#K29" target="_self">Subformulae</a> <font color="Maroon">F</font>
 <b>by </b><i><a class="ref" href="zf_lang.html#T34" target="_self">Th34</a></i>;<br/>


</div>
