for x being object holds
( x in {1,2} /\ {3,4} iff x in {} )

proof

let x be object ; :: thesis: ( x in {1,2} /\ {3,4} iff x in {} )
( x in {1,2} /\ {3,4} iff ( x in {1,2} & x in {3,4} ) ) by XBOOLE_0:def 4;
then ( x in {1,2} /\ {3,4} iff ( ( x = 1 or x = 2 ) & ( x = 3 or x = 4 ) ) ) by TARSKI:def 2;
hence ( x in {1,2} /\ {3,4} iff x in {} ) ; :: thesis: verum

end;

hence {1,2} /\ {3,4} = {} ; :: thesis: verum