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<b>let </b><font color="Maroon" title="c1">p1</font>, <font color="Maroon" title="c2">p2</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"> for <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">y1</font>, <font color="Olive" title="b3">x2</font>, <font color="Olive" title="b4">y2</font> being  <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>  st  <a href="zf_lang.html#K15" title="ZF_LANG:func.15">Ex</a> <font color="Olive" title="b1">x1</font>,<font color="Olive" title="b2">y1</font>,<font color="Maroon" title="c1">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K15" title="ZF_LANG:func.15">Ex</a> <font color="Olive" title="b3">x2</font>,<font color="Olive" title="b4">y2</font>,<font color="Maroon" title="c2">p2</font> holds <br/>( <font color="Olive" title="b1">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">x2</font> &amp; <font color="Olive" title="b2">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">y2</font> &amp; <font color="Maroon" title="c1">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p2</font> )</span><br/><b>let </b><font color="Maroon" title="c3">x1</font>, <font color="Maroon" title="c4">y1</font>, <font color="Maroon" title="c5">x2</font>, <font color="Maroon" title="c6">y2</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"> (  <a href="zf_lang.html#K15" title="ZF_LANG:func.15">Ex</a> <font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c4">y1</font>,<font color="Maroon" title="c1">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K15" title="ZF_LANG:func.15">Ex</a> <font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">y2</font>,<font color="Maroon" title="c2">p2</font> implies ( <font color="Maroon" title="c3">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x2</font> &amp; <font color="Maroon" title="c4">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">y2</font> &amp; <font color="Maroon" title="c1">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p2</font> ) )</span><br/>











<b>assume </b><a NAME="E1:13"/>
 <a href="zf_lang.html#K15" title="ZF_LANG:func.15">Ex</a> <font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c4">y1</font>,<font color="Maroon" title="c1">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K15" title="ZF_LANG:func.15">Ex</a> <font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">y2</font>,<font color="Maroon" title="c2">p2</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">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x2</font> &amp; <font color="Maroon" title="c4">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">y2</font> &amp; <font color="Maroon" title="c1">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p2</font> )</span><br/>

<a NAME="E2:13"/><b>then </b>
( <font color="Maroon" title="c3">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x2</font> &amp;  <a href="zf_lang.html#K13" title="ZF_LANG:func.13">Ex</a> <font color="Maroon" title="c4">y1</font>,<font color="Maroon" title="c1">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K13" title="ZF_LANG:func.13">Ex</a> <font color="Maroon" title="c6">y2</font>,<font color="Maroon" title="c2">p2</font> )
 
<b>by </b><i><a class="ref" href="zf_lang.html#T51" title="ZF_LANG:th.51">ZF_LANG:51</a></i>;<br/>
<b>hence </b><a NAME="E3:13"/>
( <font color="Maroon" title="c3">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x2</font> &amp; <font color="Maroon" title="c4">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">y2</font> &amp; <font color="Maroon" title="c1">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p2</font> )
 <b>by </b><i><a class="ref" href="zf_lang.html#T51" title="ZF_LANG:th.51">ZF_LANG:51</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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