let T1, T2 be Function of the carrier' of C,the carrier' of B; :: thesis: ( ( for f being Morphism of C holds T1 . f = S . (f opp ) ) & ( for f being Morphism of C holds T2 . f = S . (f opp ) ) implies T1 = T2 )
assume that
A1: for f being Morphism of C holds T1 . f = S . (f opp ) and
A2: for f being Morphism of C holds T2 . f = S . (f opp ) ; :: thesis: T1 = T2

now

let f be Morphism of C; :: thesis: T1 . f = T2 . f
thus T1 . f = S . (f opp ) by A1
.= T2 . f by A2 ; :: thesis: verum

end;

hence T1 = T2 by FUNCT_2:113; :: thesis: verum