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