Rule of Distribution/Conjunction Distributes over Disjunction/Right Distributive/Formulation 1/Forward Implication
< Rule of Distribution | Conjunction Distributes over Disjunction | Right Distributive | Formulation 1
Jump to navigation
Jump to search
Definition
- $\paren {q \lor r} \land p \vdash \paren {q \land p} \lor \paren {r \land p}$
Proof
By the tableau method of natural deduction:
Line | Pool | Formula | Rule | Depends upon | Notes | |
---|---|---|---|---|---|---|
1 | 1 | $\paren {q \lor r} \land p$ | Premise | (None) | ||
2 | 1 | $p \land \paren {q \lor r}$ | Sequent Introduction | 1 | Conjunction is Commutative | |
3 | 1 | $\paren {p \lor q} \land \paren {p \lor r}$ | Sequent Introduction | 2 | Conjunction is Left Distributive over Disjunction | |
4 | 1 | $\paren {q \land p} \lor \paren {r \land p}$ | Sequent Introduction | 3 | Conjunction is Commutative |
$\blacksquare$