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