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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E7">Th9</font></span>: <a NAME="T8"><span class="comment"><font color="firebrick">:: INTPRO_2:8</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="intpro_1.html#K1" title="INTPRO_1:func.1">MC-wff</a><br/>  for <font color="Olive" title="b2">f</font>, <font color="Olive" title="b3">g</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="intpro_1.html#K1" title="INTPRO_1:func.1">MC-wff</a>,<a href="intpro_2.html#K2" title="INTPRO_2:func.2">Proof_Step_Kinds_IPC</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>  st <font color="Olive" title="b2">f</font> <a href="intpro_2.html#R2" title="INTPRO_2:pred.2">is_a_proof_wrt_IPC</a> <font color="Olive" title="b1">X</font> &amp; <font color="Olive" title="b3">g</font> <a href="intpro_2.html#R2" title="INTPRO_2:pred.2">is_a_proof_wrt_IPC</a> <font color="Olive" title="b1">X</font> holds <br/><font color="Olive" title="b2">f</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b3">g</font> <a href="intpro_2.html#R2" title="INTPRO_2:pred.2">is_a_proof_wrt_IPC</a> <font color="Olive" title="b1">X</font></div></div>
