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