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

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

let x be object ; :: thesis: ( x in {x1,x2,x3} iff x in {x1} \/ {x2,x3} )
( x in {x1,x2,x3} iff ( x = x1 or x = x2 or x = x3 ) ) by Def1;
then ( x in {x1,x2,x3} iff ( x in {x1} or x in {x2,x3} ) ) by TARSKI:def 1, TARSKI:def 2;
hence ( x in {x1,x2,x3} iff x in {x1} \/ {x2,x3} ) by XBOOLE_0:def 3; :: thesis: verum

end;

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