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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="zf_lang.html#NM2">ZF-formula</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="zf_lang.html#NM1">Variable</a>;<br/>







<a NAME="E1:165"/>
( (  <a href="zf_lang.html#K13">Ex</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K13">Ex</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> implies  <a href="zf_lang.html#K8">All</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><a href="zf_lang.html#K6">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K8">All</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<span class="default"><a href="zf_lang.html#K6">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> ) &amp; (  <a href="zf_lang.html#K8">All</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><a href="zf_lang.html#K6">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K8">All</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<span class="default"><a href="zf_lang.html#K6">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> implies  <a href="zf_lang.html#K13">Ex</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K13">Ex</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> ) &amp; (  <a href="zf_lang.html#K6">'not'</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K6">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> implies  <a href="zf_lang.html#K8">All</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><a href="zf_lang.html#K6">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K8">All</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<span class="default"><a href="zf_lang.html#K6">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> ) &amp; (  <a href="zf_lang.html#K8">All</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><a href="zf_lang.html#K6">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K8">All</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<span class="default"><a href="zf_lang.html#K6">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> implies  <a href="zf_lang.html#K6">'not'</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K6">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> ) &amp; (  <a href="zf_lang.html#K6">'not'</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K6">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> implies <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> ) &amp; ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> implies  <a href="zf_lang.html#K6">'not'</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K6">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> ) )
 
<b>by </b><i><a class="ref" href="zf_lang1.html#T170" target="_self">Th170</a>, <a class="ref" href="zf_lang1.html#T174" target="_self">Th174</a></i>;<br/>
<b>hence </b><a NAME="E2:165"/>
(  <a href="zf_lang.html#K13">Ex</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K13">Ex</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> iff <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 ;<br/>


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