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<b>let </b><font color="Maroon" title="c1">G</font>, <font color="Maroon" title="c2">H</font> be   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>;<br/><b>let </b><font color="Maroon" title="c3">z</font>, <font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c5">y</font> be   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>;<br/>









<b>assume </b><a NAME="E1:159"/><i><font color="Green" title="E63">A1</font></i>: 
<font color="Maroon" title="c3">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">x</font>
 ;<br/>

<b>thus </b><a NAME="E2:159"/>
(  <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c3">z</font>,<font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c3">z</font>,<font color="Maroon" title="c2">H</font></span>)</span> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font> implies <font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="159_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:159_1"/>
 <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c3">z</font>,<font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c3">z</font>,<font color="Maroon" title="c2">H</font></span>)</span> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>
 ;<br/>

<a NAME="E2:159_1"/><b>then </b>
 <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c3">z</font>,<font color="Maroon" title="c1">G</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="c3">z</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span>)</span>
 
<b>by </b><i><a class="txt" href="zf_lang1.html#E1:159"><i><font color="Green" title="E63">A1</font></i></a>, <a class="txt" href="zf_lang1.html#E176"><i><font color="Green" title="E59">Lm2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:159_1"/>
<font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>
 <b>by </b><i><a class="ref" href="zf_lang.html#T12" title="ZF_LANG:th.12">ZF_LANG:12</a></i>;<br/>


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

<b>thus </b><a NAME="E3:159"/>
( <font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font> implies  <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c3">z</font>,<font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c3">z</font>,<font color="Maroon" title="c2">H</font></span>)</span> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font> )
 <b>by </b><i><a class="txt" href="zf_lang1.html#E1:159"><i><font color="Green" title="E63">A1</font></i></a>, <a class="txt" href="zf_lang1.html#E176"><i><font color="Green" title="E59">Lm2</font></i></a></i>;<br/>


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