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

<b>thus </b><a NAME="E1:58_2_1"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="zf_lang.html#V6" target="_self">universal</a> implies ex <font color="Olive">b<sub>1</sub></font> being  <a href="zf_lang.html#NM2">ZF-formula</a>ex <font color="Olive">b<sub>2</sub></font> being  <a href="zf_lang.html#NM1">Variable</a> st  <a href="zf_lang.html#K8" target="_self">All</a> <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> )
 <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">c<sub>1</sub></font> is <a href="zf_lang.html#V6" target="_self">universal</a>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>2</sub></font> being   <a href="zf_lang.html#NM1">Variable</a>, <font color="Maroon">c<sub>3</sub></font> being   <a href="zf_lang.html#NM2">ZF-formula</a><b> such that </b><br/><a NAME="E3:58_2_1_1"/><i><font color="Green">E46</font></i>: 
 <a href="zf_lang.html#K8" target="_self">All</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="zf_lang.html#D14" target="_self">Def14</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>3</sub></font>
;<br/>

<b>thus </b><a NAME="E4:58_2_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="zf_lang.html#NM1">Variable</a> st  <a href="zf_lang.html#K8" target="_self">All</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="zf_lang.html#E3:58_2_1_1"><i><font color="Green">E46</font></i></a></i>;<br/>


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

<b>thus </b><a NAME="E2:58_2_1"/>
( not <font color="Maroon">c<sub>1</sub></font> is <a href="zf_lang.html#V6" target="_self">universal</a> implies ex <font color="Olive">b<sub>1</sub></font> being  <a href="zf_lang.html#NM2">ZF-formula</a>ex <font color="Olive">b<sub>2</sub></font> being  <a href="zf_lang.html#NM1">Variable</a> st  <a href="zf_lang.html#K13" target="_self">Ex</a> <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> )
 <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">c<sub>1</sub></font> is <a href="zf_lang.html#V6" target="_self">universal</a>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>2</sub></font> being   <a href="zf_lang.html#NM1">Variable</a>, <font color="Maroon">c<sub>3</sub></font> being   <a href="zf_lang.html#NM2">ZF-formula</a><b> such that </b><br/><a NAME="E3:58_2_1_2"/><i><font color="Green">E46</font></i>: 
 <a href="zf_lang.html#K13" target="_self">Ex</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="zf_lang.html#E1:58"><i><font color="Green">E45</font></i></a>, <a class="ref" href="zf_lang.html#D23" target="_self">Def23</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>3</sub></font>
;<br/>

<b>thus </b><a NAME="E4:58_2_1_2"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="zf_lang.html#NM1">Variable</a> st  <a href="zf_lang.html#K13" target="_self">Ex</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="zf_lang.html#E3:58_2_1_2"><i><font color="Green">E46</font></i></a></i>;<br/>


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


</div>
