F = [(A + C) B + (A + C) C] + ABC [Therefore A + B = A middot B] F = [(A + C) B middot (A + C) C] + ABC [Therefore AB = A + B] F = [(A + C) B] middot [(A + C) C]] + ABC [Therefore A + B = A + B] implies [(AC + B) (AC + C)] + ABC [Therefore A + AB = A + B] implies [(AC + B) (AC + C)] + ABC [Because A + AB = A + B] implies [(AC + B) (A + C)] + ABC implies [AC + AB + BC + ABC] implies AC + AB [1 + C] + BC [Because 1 + A = 1] implies AC + AB + BC [Because Consensus theorem xy + xz + yz = xy + xz] F = BC + AC