now for x being object holds
( x in {1,2,3} \ {3} iff x in {1,2} )let x be
object ;
( x in {1,2,3} \ {3} iff x in {1,2} )
(
x in {1,2,3} \ {3} iff (
x in {1,2,3} & not
x in {3} ) )
by XBOOLE_0:def 5;
then
(
x in {1,2,3} \ {3} iff ( (
x = 1 or
x = 2 or
x = 3 ) & not
x = 3 ) )
by ENUMSET1:def 1, TARSKI:def 1;
hence
(
x in {1,2,3} \ {3} iff
x in {1,2} )
by TARSKI:def 2;
verum end;
hence
{1,2,3} \ {3} = {1,2}
by TARSKI:2; verum