<?xml version="1.0"?>
<div class="add">

<b>thus </b><a NAME="E1:58_2_1"/>
( <font color="Maroon" title="c1">H</font> is <a href="zf_lang.html#V6" title="ZF_LANG:attr.6">universal</a> implies  ex <font color="Olive" title="b1">H1</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a> ex <font color="Olive" title="b2">x</font> being  <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a> st  <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Olive" title="b2">x</font>,<font color="Olive" title="b1">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( not <font color="Maroon" title="c1">H</font> is <a href="zf_lang.html#V6" title="ZF_LANG:attr.6">universal</a> implies  ex <font color="Olive">b<sub>1</sub></font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a> ex <font color="Olive" title="b2">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="b2">x</font>,<font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_2_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:58_2_1_1"/>
<font color="Maroon" title="c1">H</font> is <a href="zf_lang.html#V6" title="ZF_LANG:attr.6">universal</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">H1</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a> ex <font color="Olive" title="b2">x</font> being  <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a> st  <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Olive" title="b2">x</font>,<font color="Olive" title="b1">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font></span><br/>

<b>then consider </b><font color="Maroon" title="c2">x</font> being   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>, <font color="Maroon" title="c3">G</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_2_1_1"/><i><font color="Green" title="E44">A2</font></i>: 
 <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font>
 <b>by </b><i><a class="ref" href="zf_lang.html#D14" target="_self" title="ZF_LANG:def.14">Def14</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c3">G</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  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#K8" title="ZF_LANG:func.8">All</a> <font color="Olive" title="b1">x</font>,<font color="Maroon" title="c3">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font></span><br/>

<b>thus </b><a NAME="E4:58_2_1_1"/>
 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#K8" title="ZF_LANG:func.8">All</a> <font color="Olive" title="b1">x</font>,<font color="Maroon" title="c3">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font>
 <b>by </b><i><a class="txt" href="zf_lang.html#E3:58_2_1_1"><i><font color="Green" title="E44">A2</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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

<b>thus </b><a NAME="E2:58_2_1"/>
( not <font color="Maroon" title="c1">H</font> is <a href="zf_lang.html#V6" title="ZF_LANG:attr.6">universal</a> implies  ex <font color="Olive" title="b1">H1</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a> ex <font color="Olive" title="b2">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="b2">x</font>,<font color="Olive" title="b1">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_2_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:58_2_1_2"/>
not <font color="Maroon" title="c1">H</font> is <a href="zf_lang.html#V6" title="ZF_LANG:attr.6">universal</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">H1</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a> ex <font color="Olive" title="b2">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="b2">x</font>,<font color="Olive" title="b1">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font></span><br/>

<b>then consider </b><font color="Maroon" title="c2">x</font> being   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>, <font color="Maroon" title="c3">G</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_2_1_2"/><i><font color="Green" title="E44">A3</font></i>: 
 <a href="zf_lang.html#K13" title="ZF_LANG:func.13">Ex</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font>
 <b>by </b><i><a class="txt" href="zf_lang.html#E1:58"><i><font color="Green" title="E43">A1</font></i></a>, <a class="ref" href="zf_lang.html#D23" target="_self" title="ZF_LANG:def.23">Def23</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c3">G</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  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">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font></span><br/>

<b>thus </b><a NAME="E4:58_2_1_2"/>
 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">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font>
 <b>by </b><i><a class="txt" href="zf_lang.html#E3:58_2_1_2"><i><font color="Green" title="E44">A3</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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


</div>
