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<b>let </b><font color="Maroon" title="c1">x</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"> for <font color="Olive" title="b1">H</font>, <font color="Olive" title="b2">H1</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>  st <font color="Olive" title="b1">H</font> is <a href="zf_lang.html#V11" title="ZF_LANG:attr.11">existential</a> holds <br/>( ( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K23" title="ZF_LANG:func.23">bound_in</a> <font color="Olive" title="b1">H</font> implies  ex <font color="Olive" title="b3">H1</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a> st  <a href="zf_lang.html#K13" title="ZF_LANG:func.13">Ex</a> <font color="Maroon" title="c1">x</font>,<font color="Olive" title="b3">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">H</font> ) &amp; (  ex <font color="Olive" title="b3">H1</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a> st  <a href="zf_lang.html#K13" title="ZF_LANG:func.13">Ex</a> <font color="Maroon" title="c1">x</font>,<font color="Olive" title="b3">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">H</font> implies <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K23" title="ZF_LANG:func.23">bound_in</a> <font color="Olive" title="b1">H</font> ) &amp; ( <font color="Olive" title="b2">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K24" title="ZF_LANG:func.24">the_scope_of</a> <font color="Olive" title="b1">H</font> implies  ex <font color="Olive" title="b3">x</font> being  <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a> st  <a href="zf_lang.html#K13" title="ZF_LANG:func.13">Ex</a> <font color="Olive" title="b3">x</font>,<font color="Olive" title="b2">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">H</font> ) &amp; (  ex <font color="Olive" title="b3">x</font> being  <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a> st  <a href="zf_lang.html#K13" title="ZF_LANG:func.13">Ex</a> <font color="Olive" title="b3">x</font>,<font color="Olive" title="b2">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">H</font> implies <font color="Olive" title="b2">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K24" title="ZF_LANG:func.24">the_scope_of</a> <font color="Olive" title="b1">H</font> ) )</span><br/><b>let </b><font color="Maroon" title="c2">H</font>, <font color="Maroon" title="c3">H1</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"> ( <font color="Maroon" title="c2">H</font> is <a href="zf_lang.html#V11" title="ZF_LANG:attr.11">existential</a> implies ( ( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K23" title="ZF_LANG:func.23">bound_in</a> <font color="Maroon" title="c2">H</font> implies  ex <font color="Olive" title="b1">H1</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a> st  <a href="zf_lang.html#K13" title="ZF_LANG:func.13">Ex</a> <font color="Maroon" title="c1">x</font>,<font color="Olive" title="b1">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H</font> ) &amp; (  ex <font color="Olive" title="b1">H1</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a> st  <a href="zf_lang.html#K13" title="ZF_LANG:func.13">Ex</a> <font color="Maroon" title="c1">x</font>,<font color="Olive" title="b1">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H</font> implies <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K23" title="ZF_LANG:func.23">bound_in</a> <font color="Maroon" title="c2">H</font> ) &amp; ( <font color="Maroon" title="c3">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K24" title="ZF_LANG:func.24">the_scope_of</a> <font color="Maroon" title="c2">H</font> implies  ex <font color="Olive" title="b1">x</font> being  <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a> st  <a href="zf_lang.html#K13" title="ZF_LANG:func.13">Ex</a> <font color="Olive" title="b1">x</font>,<font color="Maroon" title="c3">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H</font> ) &amp; (  ex <font color="Olive" title="b1">x</font> being  <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a> st  <a href="zf_lang.html#K13" title="ZF_LANG:func.13">Ex</a> <font color="Olive" title="b1">x</font>,<font color="Maroon" title="c3">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H</font> implies <font color="Maroon" title="c3">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K24" title="ZF_LANG:func.24">the_scope_of</a> <font color="Maroon" title="c2">H</font> ) ) )</span><br/>





<b>assume </b><a NAME="E1:58"/><i><font color="Green" title="E46">A1</font></i>: 
<font color="Maroon" title="c2">H</font> is <a href="zf_lang.html#V11" title="ZF_LANG:attr.11">existential</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K23" title="ZF_LANG:func.23">bound_in</a> <font color="Maroon" title="c2">H</font> implies  ex <font color="Olive" title="b1">H1</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a> st  <a href="zf_lang.html#K13" title="ZF_LANG:func.13">Ex</a> <font color="Maroon" title="c1">x</font>,<font color="Olive" title="b1">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H</font> ) &amp; (  ex <font color="Olive" title="b1">H1</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a> st  <a href="zf_lang.html#K13" title="ZF_LANG:func.13">Ex</a> <font color="Maroon" title="c1">x</font>,<font color="Olive" title="b1">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H</font> implies <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K23" title="ZF_LANG:func.23">bound_in</a> <font color="Maroon" title="c2">H</font> ) &amp; ( <font color="Maroon" title="c3">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K24" title="ZF_LANG:func.24">the_scope_of</a> <font color="Maroon" title="c2">H</font> implies  ex <font color="Olive" title="b1">x</font> being  <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a> st  <a href="zf_lang.html#K13" title="ZF_LANG:func.13">Ex</a> <font color="Olive" title="b1">x</font>,<font color="Maroon" title="c3">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H</font> ) &amp; (  ex <font color="Olive" title="b1">x</font> being  <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a> st  <a href="zf_lang.html#K13" title="ZF_LANG:func.13">Ex</a> <font color="Olive" title="b1">x</font>,<font color="Maroon" title="c3">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H</font> implies <font color="Maroon" title="c3">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K24" title="ZF_LANG:func.24">the_scope_of</a> <font color="Maroon" title="c2">H</font> ) )</span><br/>

<b>then consider </b><font color="Maroon" title="c4">y</font> being   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>, <font color="Maroon" title="c5">F</font> being   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a><b> such that </b><br/><a NAME="E3:58"/><i><font color="Green" title="E47">A2</font></i>: 
<font color="Maroon" title="c2">H</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="c4">y</font>,<font color="Maroon" title="c5">F</font>
 <b>by </b><i><a class="ref" href="zf_lang.html#D23" target="_self" title="ZF_LANG:def.23">Def23</a></i>;<br/>
<a NAME="E4:58"/>
<font color="Maroon" title="c2">H</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<b>by </b><i><a class="txt" href="#E3:58"><i><font color="Green" title="E47">A2</font></i></a>, <a class="ref" href="finseq_1.html#T58" title="FINSEQ_1:th.58">FINSEQ_1:58</a></i>;<br/>
<a NAME="E5:58"/><b>then </b>
not <font color="Maroon" title="c2">H</font> is <a href="zf_lang.html#V6" title="ZF_LANG:attr.6">universal</a>
 
<b>by </b><i><a class="ref" href="zf_lang.html#T39" target="_self" title="ZF_LANG:th.39">Th39</a></i>;<br/>
<b>hence </b><a NAME="E6:58"/>
( ( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K23" title="ZF_LANG:func.23">bound_in</a> <font color="Maroon" title="c2">H</font> implies  ex <font color="Olive" title="b1">H1</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a> st  <a href="zf_lang.html#K13" title="ZF_LANG:func.13">Ex</a> <font color="Maroon" title="c1">x</font>,<font color="Olive" title="b1">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H</font> ) &amp; (  ex <font color="Olive" title="b1">H1</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a> st  <a href="zf_lang.html#K13" title="ZF_LANG:func.13">Ex</a> <font color="Maroon" title="c1">x</font>,<font color="Olive" title="b1">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H</font> implies <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K23" title="ZF_LANG:func.23">bound_in</a> <font color="Maroon" title="c2">H</font> ) &amp; ( <font color="Maroon" title="c3">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K24" title="ZF_LANG:func.24">the_scope_of</a> <font color="Maroon" title="c2">H</font> implies  ex <font color="Olive" title="b1">x</font> being  <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a> st  <a href="zf_lang.html#K13" title="ZF_LANG:func.13">Ex</a> <font color="Olive" title="b1">x</font>,<font color="Maroon" title="c3">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H</font> ) &amp; (  ex <font color="Olive" title="b1">x</font> being  <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a> st  <a href="zf_lang.html#K13" title="ZF_LANG:func.13">Ex</a> <font color="Olive" title="b1">x</font>,<font color="Maroon" title="c3">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H</font> implies <font color="Maroon" title="c3">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K24" title="ZF_LANG:func.24">the_scope_of</a> <font color="Maroon" title="c2">H</font> ) )
 <b>by </b><i><a class="txt" href="#E1:58"><i><font color="Green" title="E46">A1</font></i></a>, <a class="ref" href="zf_lang.html#D33" target="_self" title="ZF_LANG:def.33">Def33</a>, <a class="ref" href="zf_lang.html#D34" target="_self" title="ZF_LANG:def.34">Def34</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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