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<b>thus </b><a NAME="E1:5_1_1"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">A</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( ( for <font color="Olive" title="b3">x</font>, <font color="Olive" title="b4">y</font> being  <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a> holds <br/> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">x</font> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <font color="Olive" title="b4">y</font></span>)</span>,<font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b3">x</font>,<font color="Olive" title="b4">y</font>)</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">A</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">x</font> <a href="zf_lang.html#K5" title="ZF_LANG:func.5">'in'</a> <font color="Olive" title="b4">y</font></span>)</span>,<font color="Maroon">H<sub>2</sub></font>(<font color="Olive" title="b3">x</font>,<font color="Olive" title="b4">y</font>)</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">A</font> ) ) &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c1">H</font>,<font color="Olive" title="b1">a</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">A</font> &amp; ( for <font color="Olive" title="b3">H'</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a><br/> for <font color="Olive" title="b4">a</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b3">H'</font>,<font color="Olive" title="b4">a</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">A</font> holds <br/>( ( <font color="Olive" title="b3">H'</font> <a href="zf_lang.html#NR1" title="ZF_LANG:NR.1">is_equality</a>  implies <font color="Olive" title="b4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>( <a href="zf_lang.html#K18" title="ZF_LANG:func.18">Var1</a> <font color="Olive" title="b3">H'</font>, <a href="zf_lang.html#K19" title="ZF_LANG:func.19">Var2</a> <font color="Olive" title="b3">H'</font>) ) &amp; ( <font color="Olive" title="b3">H'</font> <a href="zf_lang.html#NR2" title="ZF_LANG:NR.2">is_membership</a>  implies <font color="Olive" title="b4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>2</sub></font>( <a href="zf_lang.html#K18" title="ZF_LANG:func.18">Var1</a> <font color="Olive" title="b3">H'</font>, <a href="zf_lang.html#K19" title="ZF_LANG:func.19">Var2</a> <font color="Olive" title="b3">H'</font>) ) &amp; ( <font color="Olive" title="b3">H'</font> is <a href="zf_lang.html#V4" title="ZF_LANG:attr.4">negative</a> implies  ex <font color="Olive" title="b5">b</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Olive" title="b5">b</font>) &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K20" title="ZF_LANG:func.20">the_argument_of</a> <font color="Olive" title="b3">H'</font></span>)</span>,<font color="Olive" title="b5">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">A</font> ) ) &amp; ( <font color="Olive" title="b3">H'</font> is <a href="zf_lang.html#V5" title="ZF_LANG:attr.5">conjunctive</a> implies  ex <font color="Olive" title="b5">b</font>, <font color="Olive" title="b6">c</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>4</sub></font>(<font color="Olive" title="b5">b</font>,<font color="Olive" title="b6">c</font>) &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K21" title="ZF_LANG:func.21">the_left_argument_of</a> <font color="Olive" title="b3">H'</font></span>)</span>,<font color="Olive" title="b5">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">A</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K22" title="ZF_LANG:func.22">the_right_argument_of</a> <font color="Olive" title="b3">H'</font></span>)</span>,<font color="Olive" title="b6">c</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">A</font> ) ) &amp; ( <font color="Olive" title="b3">H'</font> is <a href="zf_lang.html#V6" title="ZF_LANG:attr.6">universal</a> implies  ex <font color="Olive" title="b5">b</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>5</sub></font>( <a href="zf_lang.html#K23" title="ZF_LANG:func.23">bound_in</a> <font color="Olive" title="b3">H'</font>,<font color="Olive" title="b5">b</font>) &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K24" title="ZF_LANG:func.24">the_scope_of</a> <font color="Olive" title="b3">H'</font></span>)</span>,<font color="Olive" title="b5">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">A</font> ) ) ) ) )
 <b>from </b><i><a class="ref" href="zf_model.html#S1" target="_self" title="ZF_MODEL:sch.1">ZF_MODEL:sch 1</a>();</i><br/>


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