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<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">x</font> be   <a href="zf_lang.html#NM1">Variable</a>;<br/><b>let </b><font color="Maroon">E</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/>





<b>thus </b><a NAME="E1:38"/>
( <font color="Maroon">E</font> <a href="zf_model.html#R2" target="_self">|=</a>  <a href="zf_lang.html#K8">All</a> <font color="Maroon">x</font>,<font color="Maroon">H</font> implies <font color="Maroon">E</font> <a href="zf_model.html#R2" target="_self">|=</a> <font color="Maroon">H</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:38_1"/><i><font color="Green">E30</font></i>: 
for <font color="Olive">f</font> being  <a href="funct_2.html#NM1">Function</a> of  <a href="zf_lang.html#K1">VAR</a> ,<font color="Maroon">E</font> holds  <font color="Maroon">E</font>,<font color="Olive">f</font> <a href="zf_model.html#R1" target="_self">|=</a>  <a href="zf_lang.html#K8">All</a> <font color="Maroon">x</font>,<font color="Maroon">H</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="zf_model.html#D5" target="_self">ZF_MODEL:def 5</a><br/>

<b>let </b><font color="Maroon">f</font> be   <a href="funct_2.html#NM1">Function</a> of  <a href="zf_lang.html#K1">VAR</a> ,<font color="Maroon">E</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="zf_model.html#D5" target="_self">ZF_MODEL:def 5</a><br/>

<a NAME="E2:38_1"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">E</font>,<font color="Maroon">f</font> <a href="zf_model.html#R1" target="_self">|=</a>  <a href="zf_lang.html#K8">All</a> <font color="Maroon">x</font>,<font color="Maroon">H</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:38_1"/>
for <font color="Olive">y</font> being  <a href="zf_lang.html#NM1">Variable</a>  st <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">y</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">y</font> holds <br/><font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Olive">y</font>
 
;<br/>
<b>hence </b><a NAME="E4:38_1"/>
<font color="Maroon">E</font>,<font color="Maroon">f</font> <a href="zf_model.html#R1" target="_self">|=</a> <font color="Maroon">H</font>
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:38"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">E</font> <a href="zf_model.html#R2" target="_self">|=</a> <font color="Maroon">H</font>
 ;<br/>

<b>let </b><font color="Maroon">f</font> be   <a href="funct_2.html#NM1">Function</a> of  <a href="zf_lang.html#K1">VAR</a> ,<font color="Maroon">E</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="zf_model.html#D5" target="_self">ZF_MODEL:def 5</a><br/>

<a NAME="E3:38"/>
for <font color="Olive">g</font> being  <a href="funct_2.html#NM1">Function</a> of  <a href="zf_lang.html#K1">VAR</a> ,<font color="Maroon">E</font>  st ( for <font color="Olive">y</font> being  <a href="zf_lang.html#NM1">Variable</a>  st <font color="Olive">g</font> <a href="funct_2.html#K3">.</a> <font color="Olive">y</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">y</font> holds <br/><font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Olive">y</font> ) holds <br/><font color="Maroon">E</font>,<font color="Olive">g</font> <a href="zf_model.html#R1" target="_self">|=</a> <font color="Maroon">H</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E4:38"/>
<font color="Maroon">E</font>,<font color="Maroon">f</font> <a href="zf_model.html#R1" target="_self">|=</a>  <a href="zf_lang.html#K8">All</a> <font color="Maroon">x</font>,<font color="Maroon">H</font>
 <b>by </b><i/>;<br/>


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