Rule of Commutation

Context
Natural deduction.

Definition
This rule is two-fold:

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

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

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

Proof
These are proved by the tableau method:

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

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