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

<b>let </b><font color="Maroon" title="c1">x</font> be   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">H</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a> holds   <a href="zf_lang.html#K29" title="ZF_LANG:func.29">Subformulae</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Olive" title="b1">H</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K29" title="ZF_LANG:func.29">Subformulae</a> <font color="Olive" title="b1">H</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Olive" title="b1">H</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><br/><b>let </b><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">  <a href="zf_lang.html#K29" title="ZF_LANG:func.29">Subformulae</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">H</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K29" title="ZF_LANG:func.29">Subformulae</a> <font color="Maroon" title="c2">H</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">H</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><br/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="104_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_lang.html#K29" title="ZF_LANG:func.29">Subformulae</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">H</font></span>)</span> implies <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K29" title="ZF_LANG:func.29">Subformulae</a> <font color="Maroon" title="c2">H</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">H</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> ) &amp; ( <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K29" title="ZF_LANG:func.29">Subformulae</a> <font color="Maroon" title="c2">H</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">H</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> implies <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_lang.html#K29" title="ZF_LANG:func.29">Subformulae</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">H</font></span>)</span> ) )</span><br/><b>thus </b><a NAME="E1:104_1"/>
( <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_lang.html#K29" title="ZF_LANG:func.29">Subformulae</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">H</font></span>)</span> implies <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K29" title="ZF_LANG:func.29">Subformulae</a> <font color="Maroon" title="c2">H</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">H</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K29" title="ZF_LANG:func.29">Subformulae</a> <font color="Maroon" title="c2">H</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">H</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> implies <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_lang.html#K29" title="ZF_LANG:func.29">Subformulae</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">H</font></span>)</span> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="104_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:104_1_1"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_lang.html#K29" title="ZF_LANG:func.29">Subformulae</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">H</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K29" title="ZF_LANG:func.29">Subformulae</a> <font color="Maroon" title="c2">H</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">H</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><br/>

<b>then consider </b><font color="Maroon" title="c4">F</font> being   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a><b> such that </b><br/><a NAME="E3:104_1_1"/><i><font color="Green" title="E83">A1</font></i>: 
( <font color="Maroon" title="c4">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c4">F</font> <a href="zf_lang.html#R2" title="ZF_LANG:pred.2">is_subformula_of</a>  <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">H</font> )
 <b>by </b><i><a class="ref" href="zf_lang.html#D42" target="_self" title="ZF_LANG:def.42">Def42</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="104_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:104_1_1_1"/>
<font color="Maroon" title="c4">F</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">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="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_lang.html#K29" title="ZF_LANG:func.29">Subformulae</a> <font color="Maroon" title="c2">H</font></span><br/><a NAME="E2:104_1_1_1"/><b>then </b>
<font color="Maroon" title="c4">F</font> <a href="zf_lang.html#R3" title="ZF_LANG:pred.3">is_proper_subformula_of</a>  <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">H</font>
 <b>by </b><i><a class="txt" href="zf_lang.html#E3:104_1_1"><i><font color="Green" title="E83">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="E3:104_1_1_1"/><b>then </b>
<font color="Maroon" title="c4">F</font> <a href="zf_lang.html#R2" title="ZF_LANG:pred.2">is_subformula_of</a> <font color="Maroon" title="c2">H</font>
 <b>by </b><i><a class="ref" href="zf_lang.html#T92" target="_self" title="ZF_LANG:th.92">Th92</a></i>;<br/><b>hence </b><a NAME="E4:104_1_1_1"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_lang.html#K29" title="ZF_LANG:func.29">Subformulae</a> <font color="Maroon" title="c2">H</font>
 <b>by </b><i><a class="txt" href="zf_lang.html#E3:104_1_1"><i><font color="Green" title="E83">A1</font></i></a>, <a class="ref" href="zf_lang.html#D42" target="_self" title="ZF_LANG:def.42">Def42</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>
<a NAME="E5:104_1_1"/><b>then </b>
( <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_lang.html#K29" title="ZF_LANG:func.29">Subformulae</a> <font color="Maroon" title="c2">H</font> or <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">H</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 
<b>by </b><i><a class="txt" href="zf_lang.html#E3:104_1_1"><i><font color="Green" title="E83">A1</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E6:104_1_1"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K29" title="ZF_LANG:func.29">Subformulae</a> <font color="Maroon" title="c2">H</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">H</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</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>assume </b><a NAME="E2:104_1"/><i><font color="Green" title="E83">A2</font></i>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K29" title="ZF_LANG:func.29">Subformulae</a> <font color="Maroon" title="c2">H</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">H</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_lang.html#K29" title="ZF_LANG:func.29">Subformulae</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">H</font></span>)</span></span><br/><div><i><font color="Green" title="E84">A3</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="104_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:104_1_2"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_lang.html#K29" title="ZF_LANG:func.29">Subformulae</a> <font color="Maroon" title="c2">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="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_lang.html#K29" title="ZF_LANG:func.29">Subformulae</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">H</font></span>)</span></span><br/><b>then consider </b><font color="Maroon" title="c4">F</font> being   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a><b> such that </b><br/><a NAME="E3:104_1_2"/><i><font color="Green" title="E85">A4</font></i>: 
( <font color="Maroon" title="c4">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c4">F</font> <a href="zf_lang.html#R2" title="ZF_LANG:pred.2">is_subformula_of</a> <font color="Maroon" title="c2">H</font> )
 <b>by </b><i><a class="ref" href="zf_lang.html#D42" target="_self" title="ZF_LANG:def.42">Def42</a></i>;<br/><a NAME="E4:104_1_2"/>
<font color="Maroon" title="c2">H</font> <a href="zf_lang.html#R1" title="ZF_LANG:pred.1">is_immediate_constituent_of</a>  <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">H</font>
 <b>by </b><i><a class="ref" href="zf_lang.html#T73" target="_self" title="ZF_LANG:th.73">Th73</a></i>;<br/><a NAME="E5:104_1_2"/><b>then </b>
<font color="Maroon" title="c2">H</font> <a href="zf_lang.html#R3" title="ZF_LANG:pred.3">is_proper_subformula_of</a>  <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">H</font>
 <b>by </b><i><a class="ref" href="zf_lang.html#T82" target="_self" title="ZF_LANG:th.82">Th82</a></i>;<br/><a NAME="E6:104_1_2"/><b>then </b>
<font color="Maroon" title="c2">H</font> <a href="zf_lang.html#R2" title="ZF_LANG:pred.2">is_subformula_of</a>  <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">H</font>
 <b>by </b><i><a class="ref" href="zf_lang.html#D41" target="_self" title="ZF_LANG:def.41">Def41</a></i>;<br/><a NAME="E7:104_1_2"/><b>then </b>
<font color="Maroon" title="c4">F</font> <a href="zf_lang.html#R2" title="ZF_LANG:pred.2">is_subformula_of</a>  <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">H</font>
 <b>by </b><i><a class="txt" href="zf_lang.html#E3:104_1_2"><i><font color="Green" title="E85">A4</font></i></a>, <a class="ref" href="zf_lang.html#T86" target="_self" title="ZF_LANG:th.86">Th86</a></i>;<br/><b>hence </b><a NAME="E8:104_1_2"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_lang.html#K29" title="ZF_LANG:func.29">Subformulae</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">H</font></span>)</span>
 <b>by </b><i><a class="txt" href="zf_lang.html#E3:104_1_2"><i><font color="Green" title="E85">A4</font></i></a>, <a class="ref" href="zf_lang.html#D42" target="_self" title="ZF_LANG:def.42">Def42</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><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="104_1_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:104_1_3"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">H</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_lang.html#K29" title="ZF_LANG:func.29">Subformulae</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">H</font></span>)</span></span><br/><a NAME="E2:104_1_3"/><b>then </b>
( <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">H</font> &amp;  <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">H</font> <a href="zf_lang.html#R2" title="ZF_LANG:pred.2">is_subformula_of</a>  <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">H</font> )
 <b>by </b><i><a class="ref" href="zf_lang.html#T79" target="_self" title="ZF_LANG:th.79">Th79</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E3:104_1_3"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_lang.html#K29" title="ZF_LANG:func.29">Subformulae</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">H</font></span>)</span>
 <b>by </b><i><a class="ref" href="zf_lang.html#D42" target="_self" title="ZF_LANG:def.42">Def42</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="E5:104_1"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_lang.html#K29" title="ZF_LANG:func.29">Subformulae</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">H</font></span>)</span>
 <b>by </b><i><a class="txt" href="zf_lang.html#E2:104_1"><i><font color="Green" title="E83">A2</font></i></a>, <a class="txt" href="zf_lang.html#E3:104_1"><i><font color="Green" title="E84">A3</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</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="E2:104"/>
 <a href="zf_lang.html#K29" title="ZF_LANG:func.29">Subformulae</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">H</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K29" title="ZF_LANG:func.29">Subformulae</a> <font color="Maroon" title="c2">H</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">H</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#T2" title="TARSKI:th.2">TARSKI:2</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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