let x1, x2, x3, x4 be object ; :: thesis: {x1,x2,x3,x4} = {x1,x2} \/ {x3,x4}

now :: thesis: for x being object holds
( x in {x1,x2,x3,x4} iff x in {x1,x2} \/ {x3,x4} )

let x be object ; :: thesis: ( x in {x1,x2,x3,x4} iff x in {x1,x2} \/ {x3,x4} )
( x in {x1,x2,x3,x4} iff ( x = x1 or x = x2 or x = x3 or x = x4 ) ) by Def2;
then ( x in {x1,x2,x3,x4} iff ( x in {x1,x2} or x in {x3,x4} ) ) by TARSKI:def 2;
hence ( x in {x1,x2,x3,x4} iff x in {x1,x2} \/ {x3,x4} ) by XBOOLE_0:def 3; :: thesis: verum

end;

hence {x1,x2,x3,x4} = {x1,x2} \/ {x3,x4} by TARSKI:2; :: thesis: verum