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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E12">Th55</font></span>: <a NAME="T55"><span class="comment"><font color="firebrick">:: ZF_LANG1:55</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">F</font>, <font color="Olive" title="b2">G</font> being   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a> holds   <a href="zf_lang.html#K28" title="ZF_LANG:func.28">Subformulae</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">F</font> <a href="zf_lang.html#K10" title="ZF_LANG:func.10">=&gt;</a> <font color="Olive" title="b2">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K28" title="ZF_LANG:func.28">Subformulae</a> <font color="Olive" title="b1">F</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K28" title="ZF_LANG:func.28">Subformulae</a> <font color="Olive" title="b2">G</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K5" title="ZF_LANG:func.5">'not'</a> <font color="Olive" title="b2">G</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">F</font> <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'&amp;'</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K5" title="ZF_LANG:func.5">'not'</a> <font color="Olive" title="b2">G</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">F</font> <a href="zf_lang.html#K10" title="ZF_LANG:func.10">=&gt;</a> <font color="Olive" title="b2">G</font></span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span></div></div>
