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The Boolean theoremĀ $$AB + \overline{A}Ā C + BC = AB + \overline{A} C$$ crresponds to
$$(A + B).(\overline{A}Ā + C).(B + C) =Ā (A + B).(\overline{A}Ā + C)$$
$$AB + \overline{A}Ā C + BC = AB + BC$$
$$AB + \overline{A} CĀ + BC = (A + B).(\overline{A}Ā + C).(B + C)$$
$$ (A + B).(\overline{A}Ā + C).(B + C) = AB + \overline{A} C$$
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