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===Rule 7===
 
===Rule 7===
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<pre>
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Rule 7
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If P, Q : U -> B,
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then the following are equivalent:
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R7a. P = Q. :R6a
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::
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R7b. P(u) = Q(u), for all u C U. :R6b
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::
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R7c. ConjUu (P(u)  =  Q(u)). :R6c
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:P1a
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::
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R7d. ConjUu (P(u) <=> Q(u)). :P1b
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::
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R7e. ConjUu (( P(u) , Q(u) )). :P1c
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:$1a
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::
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R7f. ConjUu (( P , Q ))$(u). :$1b
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</pre>
      
<br>
 
<br>
Line 2,686: Line 2,664:  
<p><math>\operatorname{R7c~:~R6c}</math></p>
 
<p><math>\operatorname{R7c~:~R6c}</math></p>
 
<p><math>\operatorname{R7c~:~P1a}</math></p>
 
<p><math>\operatorname{R7c~:~P1a}</math></p>
 +
|- style="height:20px"
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| &nbsp;
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| &nbsp;
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| &nbsp;
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| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
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|- style="height:40px"
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| &nbsp;
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| <math>\operatorname{R7d.}</math>
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| <math>\operatorname{Conj_x^X}~ (p(x) ~\Leftrightarrow~ q(x))</math>
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| style="border-left:1px solid black; text-align:center" | <math>\operatorname{R7d~:~P1b}</math>
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|- style="height:20px"
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| &nbsp;
 +
| &nbsp;
 +
| &nbsp;
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| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
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|- style="height:60px"
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| &nbsp;
 +
| <math>\operatorname{R7e.}</math>
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| <math>\operatorname{Conj_x^X}~ \underline{((}~ p(x) ~,~ q(x) ~\underline{))}</math>
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| style="border-left:1px solid black; text-align:center" |
 +
<p><math>\operatorname{R7e~:~P1c}</math></p>
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<p><math>\operatorname{R7e~:~$1a}</math></p>
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|- style="height:20px"
 +
| &nbsp;
 +
| &nbsp;
 +
| &nbsp;
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| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
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|- style="height:40px"
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| &nbsp;
 +
| <math>\operatorname{R7f.}</math>
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| <math>\operatorname{Conj_x^X}~ \underline{((}~ p ~,~ q ~\underline{))}^\$ (x)</math>
 +
| style="border-left:1px solid black; text-align:center" | <math>\operatorname{R7f~:~$1b}</math>
 
|}
 
|}
 
|}
 
|}
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