Dokazati skupovnu jednakost: A\(B\C) = (A\B) ∪ (A∩C)
x ∈ A\(B\C) <=> x ∈ A ∧ ¬(x ∈ B\C)
<=> x ∈ A ∧ ¬(x ∈ B ∧ ¬(x ∈ C))
<=> x ∈ A ∧ (¬(x ∈ B) ∨ ¬(¬(x ∈ C))) (DeMorganov zakon)
<=> x ∈ A ∧ (¬(x ∈ B) ∨ x ∈ C) (dvojna negacija)
<=> ( x ∈ A ∧ ¬(x ∈ B) ) ∨ ( x ∈ A ∧ x ∈ C ) (distributivnost konjukcije prema disjunkciji)
<=> ( x ∈ A\B ) ∨ ( x ∈ A∩C )
<=> x ∈ (A\B) ∪ (A∩C)