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<div><span class="kw">theorem </span><a NAME="T11"><span class="comment"><font color="firebrick">:: ZF_MODEL:11</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">H</font> being   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a><br/>  for <font color="Olive" title="b2">E</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">H</font> is  <a href="zf_lang.html#V6" title="ZF_LANG:attr.6">universal</a>  holds <br/> for <font color="Olive" title="b3">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="zf_lang.html#K1" title="ZF_LANG:func.1">VAR</a>,<font color="Olive" title="b2">E</font> holds <br/> ( ( <font color="Olive" title="b3">f</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K5" title="ZF_MODEL:func.5">St</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K23" title="ZF_LANG:func.23">the_scope_of</a> <font color="Olive" title="b1">H</font></span>)</span>,<font color="Olive" title="b2">E</font>) &amp; (  for <font color="Olive" title="b4">g</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="zf_lang.html#K1" title="ZF_LANG:func.1">VAR</a>,<font color="Olive" title="b2">E</font>  st (  for <font color="Olive" title="b5">y</font> being   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>  st <font color="Olive" title="b4">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b5">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b5">y</font> holds <br/> <a href="zf_lang.html#K22" title="ZF_LANG:func.22">bound_in</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">y</font> ) holds <br/><font color="Olive" title="b4">g</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K5" title="ZF_MODEL:func.5">St</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K23" title="ZF_LANG:func.23">the_scope_of</a> <font color="Olive" title="b1">H</font></span>)</span>,<font color="Olive" title="b2">E</font>) ) ) iff <font color="Olive" title="b3">f</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K5" title="ZF_MODEL:func.5">St</a> (<font color="Olive" title="b1">H</font>,<font color="Olive" title="b2">E</font>) )</div></div>
