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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Y</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:97_1_2"/><i><font color="Green">E35</font></i>: 
for <font color="Olive">a</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> iff  ex <font color="Olive">F</font> being  <a href="zf_lang.html#NM2">ZF-formula</a> st <br/>( <font color="Olive">F</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> &amp; <font color="Olive">F</font> <a href="zf_lang.html#R2" target="_self">is_subformula_of</a> <font color="Maroon">H</font> ) )
 <b>and </b><br/><a NAME="E2:97_1_2"/><i><font color="Green">E36</font></i>: 
for <font color="Olive">a</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> iff  ex <font color="Olive">F</font> being  <a href="zf_lang.html#NM2">ZF-formula</a> st <br/>( <font color="Olive">F</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> &amp; <font color="Olive">F</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="97_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>thus </b><a NAME="E1:97_1_2_1"/>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> implies <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1_2_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:97_1_2_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ;<br/>

<a NAME="E2:97_1_2_1_1"/><b>then </b>
 ex <font color="Olive">F</font> being  <a href="zf_lang.html#NM2">ZF-formula</a> st <br/>( <font color="Olive">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Olive">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#T34" target="_self">Th34</a></i>;<br/>
<b>hence </b><a NAME="E3:97_1_2_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 <b>by </b><i><a class="ref" href="zf_lang.html#T35" target="_self">Th35</a></i>;<br/>


</div><b>end;</b></div><b>assume </b><a NAME="E2:97_1_2_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 ;<br/><a NAME="E3:97_1_2_1"/><b>then </b>
 ex <font color="Olive">F</font> being  <a href="zf_lang.html#NM2">ZF-formula</a> st <br/>( <font color="Olive">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Olive">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#T35" target="_self">Th35</a></i>;<br/><b>hence </b><a NAME="E4:97_1_2_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="zf_lang.html#T34" target="_self">Th34</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:97_1_2"/>
<font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Y</font>
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>


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