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

let x be object ; :: thesis: ( x in {1,2,3,4} /\ {4} iff x in {4} )
( x in {1,2,3,4} /\ {4} iff ( x in {1,2,3,4} & x in {4} ) ) by XBOOLE_0:def 4;
then ( x in {1,2,3,4} /\ {4} iff x = 4 ) by TARSKI:def 1, ENUMSET1:def 2;
hence ( x in {1,2,3,4} /\ {4} iff x in {4} ) by TARSKI:def 1; :: thesis: verum

end;

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