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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E24">Th14</font></span>: <a NAME="T13"><span class="comment"><font color="firebrick">:: INTPRO_2:13</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">Y</font>, <font color="Olive" title="b2">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>  st <font color="Olive" title="b1">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b3">p</font> where <font color="Olive" title="b3">p</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="intpro_1.html#K1" title="INTPRO_1:func.1">MC-wff</a>  :  ex <font color="Olive" title="b4">f</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 <br/>( <font color="Olive" title="b4">f</font> <a href="intpro_2.html#R2" title="INTPRO_2:pred.2">is_a_proof_wrt_IPC</a> <font color="Olive" title="b2">X</font> &amp;  <a href="intpro_2.html#K3" title="INTPRO_2:func.3">Effect_IPC</a> <font color="Olive" title="b4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">p</font> ) </span> } </span>  holds <br/><font color="Olive" title="b1">Y</font> is  <a href="intpro_1.html#V8" title="INTPRO_1:attr.8">IPC_theory</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="intpro_2.html#E19"><span class="lab"><font color="Green" title="E14">Lm2</font></span></a>, <a class="txt" href="intpro_2.html#E20"><span class="lab"><font color="Green" title="E15">Lm3</font></span></a>, <a class="txt" href="intpro_2.html#E21"><span class="lab"><font color="Green" title="E16">Lm4</font></span></a>, <a class="txt" href="intpro_2.html#E22"><span class="lab"><font color="Green" title="E17">Lm5</font></span></a>, <a class="txt" href="intpro_2.html#E23"><span class="lab"><font color="Green" title="E18">Lm6</font></span></a>, <a class="txt" href="intpro_2.html#E24"><span class="lab"><font color="Green" title="E19">Lm7</font></span></a>, <a class="txt" href="intpro_2.html#E25"><span class="lab"><font color="Green" title="E20">Lm8</font></span></a>, <a class="txt" href="intpro_2.html#E26"><span class="lab"><font color="Green" title="E21">Lm9</font></span></a>, <a class="txt" href="intpro_2.html#E27"><span class="lab"><font color="Green" title="E22">Lm10</font></span></a>, <a class="txt" href="intpro_2.html#E28"><span class="lab"><font color="Green" title="E23">Lm11</font></span></a></span>;<br/></div></div>
