Absorption Laws (Logic)/Conjunction Absorbs Disjunction/Forward Implication
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Theorem
- $p \land \paren {p \lor q} \vdash p$
Proof
By the tableau method of natural deduction:
Line | Pool | Formula | Rule | Depends upon | Notes | |
---|---|---|---|---|---|---|
1 | 1 | $p \land \paren {p \lor q}$ | Premise | (None) | ||
2 | 1 | $p$ | Rule of Simplification: $\land \EE_1$ | 1 |
$\blacksquare$
Sources
- 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): Chapter $1$: The Propositional Calculus $1$: $5$ Further Proofs: Résumé of Rules: Theorems $31 \ \text{(a)}$