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<span class="kw">let </span><font color="Maroon" title="c1">p</font>, <font color="Maroon" title="c2">q</font> be   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font>, <font color="Olive" title="b4">t</font>, <font color="Olive" title="b5">s</font> being   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>  st  <a href="zf_lang.html#K17" title="ZF_LANG:func.17">Ex</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>,<font color="Olive" title="b3">z</font>,<font color="Maroon" title="c1">p</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="b4">t</font>,<font color="Olive" title="b5">s</font>,<font color="Maroon" title="c2">q</font>) holds <br/>( <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">t</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">s</font> &amp;  <a href="zf_lang.html#K13" title="ZF_LANG:func.13">Ex</a> (<font color="Olive" title="b3">z</font>,<font color="Maroon" title="c1">p</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">q</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</font>, <font color="Maroon" title="c5">z</font>, <font color="Maroon" title="c6">t</font>, <font color="Maroon" title="c7">s</font> be   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="zf_lang.html#K17" title="ZF_LANG:func.17">Ex</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c1">p</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="c6">t</font>,<font color="Maroon" title="c7">s</font>,<font color="Maroon" title="c2">q</font>) implies ( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">t</font> &amp; <font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">s</font> &amp;  <a href="zf_lang.html#K13" title="ZF_LANG:func.13">Ex</a> (<font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c1">p</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">q</font> ) )</span><br/>













<a NAME="E1:15"/>
 <a href="zf_lang.html#K17" title="ZF_LANG:func.17">Ex</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c1">p</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="c3">x</font>,<font color="Maroon" title="c4">y</font>,<span class="p1">(<span class="default"><a href="zf_lang.html#K13" title="ZF_LANG:func.13">Ex</a> (<font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c1">p</font>)</span>)</span>)
 
;<br/>
<span class="kw">hence </span><a NAME="E2:15"/>
(  <a href="zf_lang.html#K17" title="ZF_LANG:func.17">Ex</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c1">p</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="c6">t</font>,<font color="Maroon" title="c7">s</font>,<font color="Maroon" title="c2">q</font>) implies ( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">t</font> &amp; <font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">s</font> &amp;  <a href="zf_lang.html#K13" title="ZF_LANG:func.13">Ex</a> (<font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c1">p</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">q</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang1.html#T17" target="_self" title="ZF_LANG1:th.17">Th20</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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