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<b>let </b><font color="Maroon" title="c1">G1</font>, <font color="Maroon" title="c2">G2</font>, <font color="Maroon" title="c3">H1</font>, <font color="Maroon" title="c4">H2</font> be   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>;<br/><b>let </b><font color="Maroon" title="c5">x</font>, <font color="Maroon" title="c6">y</font> be   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>;<br/>











<a NAME="E1:162"/>
( ( <font color="Maroon" title="c1">G1</font> <a href="zf_lang.html#K12" title="ZF_LANG:func.12">&lt;=&gt;</a> <font color="Maroon" title="c2">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">H1</font> <a href="zf_lang.html#K12" title="ZF_LANG:func.12">&lt;=&gt;</a> <font color="Maroon" title="c4">H2</font></span>)</span> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font> implies ( <font color="Maroon" title="c1">G1</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c2">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">H1</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c4">H2</font></span>)</span> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font> &amp; <font color="Maroon" title="c2">G2</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c1">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H2</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c3">H1</font></span>)</span> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font> ) ) &amp; ( <font color="Maroon" title="c1">G1</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c2">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">H1</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c4">H2</font></span>)</span> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font> &amp; <font color="Maroon" title="c2">G2</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c1">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H2</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c3">H1</font></span>)</span> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font> implies <font color="Maroon" title="c1">G1</font> <a href="zf_lang.html#K12" title="ZF_LANG:func.12">&lt;=&gt;</a> <font color="Maroon" title="c2">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">H1</font> <a href="zf_lang.html#K12" title="ZF_LANG:func.12">&lt;=&gt;</a> <font color="Maroon" title="c4">H2</font></span>)</span> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font> ) &amp; ( <font color="Maroon" title="c1">G1</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c2">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">H1</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c4">H2</font></span>)</span> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font> implies ( <font color="Maroon" title="c1">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H1</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font> &amp; <font color="Maroon" title="c2">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">H2</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font> ) ) &amp; ( <font color="Maroon" title="c1">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H1</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font> &amp; <font color="Maroon" title="c2">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">H2</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font> implies <font color="Maroon" title="c1">G1</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c2">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">H1</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c4">H2</font></span>)</span> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font> ) &amp; ( <font color="Maroon" title="c2">G2</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c1">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H2</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c3">H1</font></span>)</span> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font> implies ( <font color="Maroon" title="c1">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H1</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font> &amp; <font color="Maroon" title="c2">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">H2</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font> ) ) &amp; ( <font color="Maroon" title="c1">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H1</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font> &amp; <font color="Maroon" title="c2">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">H2</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font> implies <font color="Maroon" title="c2">G2</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c1">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H2</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <font color="Maroon" title="c3">H1</font></span>)</span> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font> ) )
 
<b>by </b><i><a class="ref" href="zf_lang1.html#T172" target="_self" title="ZF_LANG1:th.172">Th172</a>, <a class="ref" href="zf_lang1.html#T176" target="_self" title="ZF_LANG1:th.176">Th176</a></i>;<br/>
<b>hence </b><a NAME="E2:162"/>
( <font color="Maroon" title="c1">G1</font> <a href="zf_lang.html#K12" title="ZF_LANG:func.12">&lt;=&gt;</a> <font color="Maroon" title="c2">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">H1</font> <a href="zf_lang.html#K12" title="ZF_LANG:func.12">&lt;=&gt;</a> <font color="Maroon" title="c4">H2</font></span>)</span> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font> iff ( <font color="Maroon" title="c1">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H1</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font> &amp; <font color="Maroon" title="c2">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">H2</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font> ) )
 ;<br/>


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