Let L Be A Distributive Lattice With 0 And 1 Prove If A Has A Complement Of A

In Boolean algebra, is there any proof of A+BC=(A+B) (A+C) other than through truth tables?

LHS = A + BC = A.1 + BC  ,using A.1 = A                           = A(1 + B) + BC ,using  1+B = 1                           =A + AB +BC                           =A(1 + C) +AB +BC , using  1+C = 1                           =A + AC +AB +BC                            =A*A + AC + AB + BC ,using A*A=A                           =(A+B) (A+C) =RHS