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<div><span class="kw">theorem </span><a NAME="T23"><span class="comment"><font color="firebrick">:: PROOFS_1:23</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">P</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="proofs_1.html#L1" title="PROOFS_1:struct.1">ProofSystem</a> <br/>  for <font color="Olive" title="b2">B</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">P</font>  st <font color="Olive" title="b1">P</font> is  <a href="proofs_1.html#V10" title="PROOFS_1:attr.10">consistent</a>  &amp;  not <font color="Olive" title="b1">P</font> is  <a href="proofs_1.html#V12" title="PROOFS_1:attr.12">paraconsistent</a>  &amp; <font color="Olive" title="b2">B</font> is  <a href="proofs_1.html#V11" title="PROOFS_1:attr.11">consistent</a>  holds <br/> ex <font color="Olive" title="b3">B1</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">P</font> st <br/>( <font color="Olive" title="b2">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">B1</font> &amp; <font color="Olive" title="b3">B1</font> is  <a href="proofs_1.html#V17" title="PROOFS_1:attr.17">maximally-consistent</a>  )</div></div>
