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





<b>assume </b><a NAME="E1:84"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">F</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">H</font> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:84_1"/>
<font color="Maroon">F</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">G</font>
 ;<br/><a NAME="E2:84_1"/><b>then </b><i><font color="Green">E32</font></i>: 
<font color="Maroon">F</font> <a href="zf_lang.html#R3" target="_self">is_proper_subformula_of</a> <font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="zf_lang.html#T26" target="_self">Th26</a>, <a class="ref" href="zf_lang.html#D14" target="_self">Def14</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:84_1_1"/>
<font color="Maroon">G</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">H</font>
 ;<br/><a NAME="E2:84_1_1"/><b>then </b>
<font color="Maroon">G</font> <a href="zf_lang.html#R3" target="_self">is_proper_subformula_of</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="ref" href="zf_lang.html#T26" target="_self">Th26</a>, <a class="ref" href="zf_lang.html#D14" target="_self">Def14</a></i>;<br/><a NAME="E3:84_1_1"/><b>then </b>
<font color="Maroon">F</font> <a href="zf_lang.html#R3" target="_self">is_proper_subformula_of</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="ref" href="zf_lang.html#T27" target="_self">Th27</a>, <a class="ref" href="zf_lang.html#D23" target="_self">Def23</a></i>;<br/><b>hence </b><a NAME="E4:84_1_1"/>
<font color="Maroon">F</font> <a href="zf_lang.html#R2" target="_self">is_subformula_of</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="ref" href="zf_lang.html#D14" target="_self">Def14</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:84_1"/>
<font color="Maroon">F</font> <a href="zf_lang.html#R2" target="_self">is_subformula_of</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="ref" href="zf_lang.html#T26" target="_self">Th26</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:84"/>
<font color="Maroon">F</font> <a href="zf_lang.html#R2" target="_self">is_subformula_of</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="ref" href="zf_lang.html#T26" target="_self">Th26</a></i>;<br/>


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