<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T42"><span class="comment"><font color="firebrick">:: ZF_LANG:42</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">x</font> being   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a><br/>  for <font color="Olive" title="b2">H</font>, <font color="Olive" title="b3">H1</font> being   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>  st <font color="Olive" title="b2">H</font> is  <a href="zf_lang.html#V6" title="ZF_LANG:attr.6">universal</a>  holds <br/>( ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K22" title="ZF_LANG:func.22">bound_in</a> <font color="Olive" title="b2">H</font> implies  ex <font color="Olive" title="b4">H1</font> being   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a> st  <a href="zf_lang.html#K7" title="ZF_LANG:func.7">All</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b4">H1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">H</font> ) &amp; (  ex <font color="Olive" title="b4">H1</font> being   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a> st  <a href="zf_lang.html#K7" title="ZF_LANG:func.7">All</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b4">H1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">H</font> implies <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K22" title="ZF_LANG:func.22">bound_in</a> <font color="Olive" title="b2">H</font> ) &amp; ( <font color="Olive" title="b3">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K23" title="ZF_LANG:func.23">the_scope_of</a> <font color="Olive" title="b2">H</font> implies  ex <font color="Olive" title="b4">x</font> being   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a> st  <a href="zf_lang.html#K7" title="ZF_LANG:func.7">All</a> (<font color="Olive" title="b4">x</font>,<font color="Olive" title="b3">H1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">H</font> ) &amp; (  ex <font color="Olive" title="b4">x</font> being   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a> st  <a href="zf_lang.html#K7" title="ZF_LANG:func.7">All</a> (<font color="Olive" title="b4">x</font>,<font color="Olive" title="b3">H1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">H</font> implies <font color="Olive" title="b3">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K23" title="ZF_LANG:func.23">the_scope_of</a> <font color="Olive" title="b2">H</font> ) ) <span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang.html#D33" target="_self" onmouseover="rs('zf_lang/D33')" onmouseout="rh()">Def33</a>, <a class="ref" href="zf_lang.html#D34" target="_self" onmouseover="rs('zf_lang/D34')" onmouseout="rh()">Def34</a></span>;<br/></div></div>
