(P ⊃ Q) ≡ [P ⊃ (Q ∨ ∼P)]

(~P ∨ Q) ≡ [~P ∨ (Q ∨ ~P)]  by using material implication on both sides 

(~P ∨ Q) ≡ [~P ∨ (~P ∨ Q)]  by using commutation on "(Q ∨ ∼P)"

(~P ∨ Q) ≡ [(~P ∨ ~P) ∨ Q]  by using association on the right side.

(~P ∨ Q) ≡ (~P ∨ Q)  by using the idempotent law on ~P ∨ ~P

Edwin