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