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<div><div><a NAME="S1"><span class="kw">scheme  </span><span class="comment"><font color="firebrick">:: PL_AXIOM:sch 1</font></span><br/></a><span class="lab"><font color="Green" title="E1">PLInd</font></span>{ <font color="Maroon">P<sub>1</sub></font>[   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ] } :<br/><div class="add"><a NAME="E4:30"/>
 for <font color="Olive" title="b1">r</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="pl_axiom.html#K1" title="PL_AXIOM:func.1">PL-WFF</a>  holds  <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">r</font>]
 </div><span class="kw">provided</span><div class="add"><a NAME="E1:30"/><span class="lab"><font color="Green" title="E22">A1</font></span>: 
<font color="Maroon">P<sub>1</sub></font>[ <a href="pl_axiom.html#K2" title="PL_AXIOM:func.2">FaLSUM</a> ]
 <span class="kw">and </span><br/><a NAME="E2:30"/><span class="lab"><font color="Green" title="E23">A2</font></span>: 
 for <font color="Olive" title="b1">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  holds  <font color="Maroon">P<sub>1</sub></font>[ <a href="pl_axiom.html#K4" title="PL_AXIOM:func.4">Prop</a> <font color="Olive" title="b1">n</font>]
 <span class="kw">and </span><br/><a NAME="E3:30"/><span class="lab"><font color="Green" title="E24">A3</font></span>: 
 for <font color="Olive" title="b1">r</font>, <font color="Olive" title="b2">s</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="pl_axiom.html#K1" title="PL_AXIOM:func.1">PL-WFF</a>   st <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">r</font>] &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b2">s</font>] holds <br/><font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">r</font> <a href="pl_axiom.html#K3" title="PL_AXIOM:func.3">=&gt;</a> <font color="Olive" title="b2">s</font>]
 </div></div></div>
