set X = B \ A;
set Y = A /\ C;
( B \ A misses A & A /\ C c= A ) by XBOOLE_1:79;
then B \ A misses A /\ C by XBOOLE_1:63;
hence for b₁ being set st b₁ = (B \ A) /\ (A /\ C) holds
b₁ is empty by XBOOLE_0:def 7; :: thesis: verum