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<div><span class="kw">theorem </span><a NAME="T51"><span class="comment"><font color="firebrick">:: ZF_LANG1:51</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">x</font> being   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a> holds <br/> (  <a href="zf_lang.html#K7" title="ZF_LANG:func.7">All</a> (<font color="Olive" title="b2">x</font>,<span class="p1">(<span class="default"><a href="zf_lang.html#K5" title="ZF_LANG:func.5">'not'</a> <font color="Olive" title="b1">H</font></span>)</span>) <a href="zf_lang.html#R3" title="ZF_LANG:pred.3">is_proper_subformula_of</a>  <a href="zf_lang.html#K12" title="ZF_LANG:func.12">Ex</a> (<font color="Olive" title="b2">x</font>,<font color="Olive" title="b1">H</font>) &amp;  <a href="zf_lang.html#K5" title="ZF_LANG:func.5">'not'</a> <font color="Olive" title="b1">H</font> <a href="zf_lang.html#R3" title="ZF_LANG:pred.3">is_proper_subformula_of</a>  <a href="zf_lang.html#K12" title="ZF_LANG:func.12">Ex</a> (<font color="Olive" title="b2">x</font>,<font color="Olive" title="b1">H</font>) )</div></div>
