let o1, o2 be UnOp of {0,1,2}; :: thesis: ( ( for a being Element of {0,1,2} holds o1 . a = - a ) & ( for a being Element of {0,1,2} holds o2 . a = - a ) implies o1 = o2 )
assume that
A5: for a being Element of {0,1,2} holds o1 . a = - a and
A6: for a being Element of {0,1,2} holds o2 . a = - a ; :: thesis: o1 = o2

now :: thesis: for a being Element of {0,1,2} holds o1 . a = o2 . a

let a be Element of {0,1,2}; :: thesis: o1 . a = o2 . a
thus o1 . a = - a by A5
.= o2 . a by A6 ; :: thesis: verum

end;

hence o1 = o2 by FUNCT_2:63; :: thesis: verum