Rule of Commutation

Context
Natural deduction.

Definition
This rule is two-fold:


 * Conjunction is commutative:
 * 1) $$p \land q \vdash q \land p$$


 * Disjunction is commutative:
 * 1) $$p \lor q \vdash q \lor p$$

Its abbreviation in a tableau proof is $$\textrm{Comm}$$.

Proof
These are proved by the tableau method:

$$p \land q \vdash q \land p$$:

$$p \lor q \vdash q \lor p$$: