let E be set ; for A, B being Subset of E st ( for x being Element of E holds
( ( x in A & not x in B ) or ( x in B & not x in A ) ) ) holds
A = B `
let A, B be Subset of E; ( ( for x being Element of E holds
( ( x in A & not x in B ) or ( x in B & not x in A ) ) ) implies A = B ` )
assume
for x being Element of E holds
( ( x in A & not x in B ) or ( x in B & not x in A ) )
; A = B `
then
for x being Element of E holds
( x in A iff not x in B )
;
hence
A = B `
by Th30; verum