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<b>let </b><font color="Maroon" title="c1">F</font>, <font color="Maroon" title="c2">G</font>, <font color="Maroon" title="c3">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"> ( <font color="Maroon" title="c1">F</font> <a href="zf_lang.html#R2" title="ZF_LANG:pred.2">is_subformula_of</a> <font color="Maroon" title="c2">G</font> &amp; <font color="Maroon" title="c2">G</font> <a href="zf_lang.html#R2" title="ZF_LANG:pred.2">is_subformula_of</a> <font color="Maroon" title="c3">H</font> implies <font color="Maroon" title="c1">F</font> <a href="zf_lang.html#R2" title="ZF_LANG:pred.2">is_subformula_of</a> <font color="Maroon" title="c3">H</font> )</span><br/>





<b>assume </b><a NAME="E1:84"/><i><font color="Green" title="E69">A1</font></i>: 
( <font color="Maroon" title="c1">F</font> <a href="zf_lang.html#R2" title="ZF_LANG:pred.2">is_subformula_of</a> <font color="Maroon" title="c2">G</font> &amp; <font color="Maroon" title="c2">G</font> <a href="zf_lang.html#R2" title="ZF_LANG:pred.2">is_subformula_of</a> <font color="Maroon" title="c3">H</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">F</font> <a href="zf_lang.html#R2" title="ZF_LANG:pred.2">is_subformula_of</a> <font color="Maroon" title="c3">H</font></span><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" title="c1">F</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">G</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">F</font> <a href="zf_lang.html#R2" title="ZF_LANG:pred.2">is_subformula_of</a> <font color="Maroon" title="c3">H</font></span><br/><a NAME="E2:84_1"/><b>then </b><i><font color="Green" title="E70">A2</font></i>: 
<font color="Maroon" title="c1">F</font> <a href="zf_lang.html#R3" title="ZF_LANG:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c2">G</font>
 <b>by </b><i><a class="txt" href="zf_lang.html#E1:84"><i><font color="Green" title="E69">A1</font></i></a>, <a class="ref" href="zf_lang.html#D41" target="_self" title="ZF_LANG:def.41">Def41</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" title="c2">G</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">H</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">F</font> <a href="zf_lang.html#R2" title="ZF_LANG:pred.2">is_subformula_of</a> <font color="Maroon" title="c3">H</font></span><br/><a NAME="E2:84_1_1"/><b>then </b>
<font color="Maroon" title="c2">G</font> <a href="zf_lang.html#R3" title="ZF_LANG:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c3">H</font>
 <b>by </b><i><a class="txt" href="zf_lang.html#E1:84"><i><font color="Green" title="E69">A1</font></i></a>, <a class="ref" href="zf_lang.html#D41" target="_self" title="ZF_LANG:def.41">Def41</a></i>;<br/><a NAME="E3:84_1_1"/><b>then </b>
<font color="Maroon" title="c1">F</font> <a href="zf_lang.html#R3" title="ZF_LANG:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c3">H</font>
 <b>by </b><i><a class="txt" href="zf_lang.html#E2:84_1"><i><font color="Green" title="E70">A2</font></i></a>, <a class="ref" href="zf_lang.html#T85" target="_self" title="ZF_LANG:th.85">Th85</a></i>;<br/><b>hence </b><a NAME="E4:84_1_1"/>
<font color="Maroon" title="c1">F</font> <a href="zf_lang.html#R2" title="ZF_LANG:pred.2">is_subformula_of</a> <font color="Maroon" title="c3">H</font>
 <b>by </b><i><a class="ref" href="zf_lang.html#D41" target="_self" title="ZF_LANG:def.41">Def41</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><b>end;</b></div><b>hence </b><a NAME="E4:84_1"/>
<font color="Maroon" title="c1">F</font> <a href="zf_lang.html#R2" title="ZF_LANG:pred.2">is_subformula_of</a> <font color="Maroon" title="c3">H</font>
 <b>by </b><i><a class="txt" href="zf_lang.html#E1:84"><i><font color="Green" title="E69">A1</font></i></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><b>end;</b></div>
<b>hence </b><a NAME="E3:84"/>
<font color="Maroon" title="c1">F</font> <a href="zf_lang.html#R2" title="ZF_LANG:pred.2">is_subformula_of</a> <font color="Maroon" title="c3">H</font>
 <b>by </b><i><a class="txt" href="zf_lang.html#E1:84"><i><font color="Green" title="E69">A1</font></i></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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