let A3, A4 be SetSequence of X; :: thesis: ( ( for n being Nat holds A3 . n = A \ (A1 . n) ) & ( for n being Nat holds A4 . n = A \ (A1 . n) ) implies A3 = A4 )
assume that
A8: for n being Nat holds A3 . n = A \ (A1 . n) and
A9: for n being Nat holds A4 . n = A \ (A1 . n) ; :: thesis: A3 = A4
let n be Element of NAT ; :: according to FUNCT_2:def 8 :: thesis: A3 . n = A4 . n
thus A3 . n = A \ (A1 . n) by A8
.= A4 . n by A9 ; :: thesis: verum