SD Derivation Rules
$`\&\text{'}$ Rules
Conjunction Introduction $(\text{&I})$
$\mathscr{P}$ | |
$\mathscr{Q}$ | |
$\rhd$ | $\mathscr{P}\,\&\,\mathscr{Q}$ |
Conjunction Elimination $(\text{&E})$
$\mathscr{P}\,\&\,\mathscr{Q}$ | |
$\rhd$ | $\mathscr{P}$ |
$\mathscr{P}\,\&\,\mathscr{Q}$ | |
$\rhd$ | $\mathscr{Q}$ |
$`\,\supset\!\text{'}$ Rules
Conditional Introduction $(\supset\text{I})$
$\mathscr{P}$ | ||
$\mathscr{Q}$ | ||
$\rhd$ | $\mathscr{P}\supset\mathscr{Q}$ |
Conditional Elimination $(\supset\text{E})$
$\mathscr{P}\supset\mathscr{Q}$ | |
$\mathscr{P}$ | |
$\rhd$ | $\mathscr{Q}$ |
$`\,\sim\!\text{'}$ Rules
Negation Introduction $(\sim\text{I})$
$\mathscr{P}$ | ||
$\mathscr{Q}$ | ||
$\sim\mathscr{Q}$ | ||
$\rhd$ | $\sim\mathscr{P}$ |
Negation Elimination $(\sim\text{E})$
$\sim\mathscr{P}$ | ||
$\mathscr{Q}$ | ||
$\sim\mathscr{Q}$ | ||
$\rhd$ | $\mathscr{P}$ |
$`\lor\text{'}$ Rules
Disjunction Introduction $(\lor\text{I})$
$\mathscr{P}$ | |
$\rhd$ | $\mathscr{P}\lor\mathscr{Q}$ |
$\mathscr{Q}$ | |
$\rhd$ | $\mathscr{Q}\lor\mathscr{P}$ |
Disjunction Elimination $(\lor\text{E})$
$\mathscr{P}\lor\mathscr{Q}$ | ||
$\mathscr{P}$ | ||
$\mathscr{R}$ | ||
$\mathscr{Q}$ | ||
$\mathscr{R}$ | ||
$\rhd$ | $\mathscr{R}$ |
$`\,\equiv\!\text{'}$ Rules
Biconditional Introduction $(\equiv\text{I})$
$\mathscr{P}$ | ||
$\mathscr{Q}$ | ||
$\mathscr{Q}$ | ||
$\mathscr{P}$ | ||
$\rhd$ | $\mathscr{P}\equiv\mathscr{Q}$ |
Biconditional Elimination $(\equiv\text{E})$
$\mathscr{P}\equiv\mathscr{Q}$ | |
$\mathscr{P}$ | |
$\rhd$ | $\mathscr{Q}$ |
$\mathscr{P}\equiv\mathscr{Q}$ | |
$\mathscr{Q}$ | |
$\rhd$ | $\mathscr{P}$ |