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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E29">Th70</font></span>: <a NAME="T24"><span class="comment"><font color="firebrick">:: GRZLOG_1:24</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="grzlog_1.html#K13" title="GRZLOG_1:func.13">GRZ-formula-set</a><br/>  for <font color="Olive" title="b2">t</font>, <font color="Olive" title="b3">u</font> being   <a href="grzlog_1.html#NM2" title="GRZLOG_1:NM.2">GRZ-formula</a>  st  <a href="grzlog_1.html#K21" title="GRZLOG_1:func.21">GRZ-axioms</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">A</font> &amp; <font color="Olive" title="b1">A</font>, <a href="grzlog_1.html#K29" title="GRZLOG_1:func.29">GRZ-rules</a>  <a href="grzlog_1.html#R2" title="GRZLOG_1:pred.2">|-</a> <font color="Olive" title="b2">t</font> <a href="grzlog_1.html#K17" title="GRZLOG_1:func.17">'='</a> <font color="Olive" title="b3">u</font> holds <br/><font color="Olive" title="b1">A</font>, <a href="grzlog_1.html#K29" title="GRZLOG_1:func.29">GRZ-rules</a>  <a href="grzlog_1.html#R2" title="GRZLOG_1:pred.2">|-</a> <font color="Olive" title="b3">u</font> <a href="grzlog_1.html#K17" title="GRZLOG_1:func.17">'='</a> <font color="Olive" title="b2">t</font></div></div>
