let f, g be BCI-homomorphism of X,(X ./. RI); :: thesis: ( ( for x being Element of X holds f . x = Class RI,x ) & ( for x being Element of X holds g . x = Class RI,x ) implies f = g )
assume that
A3: for x being Element of X holds f . x = Class RI,x and
A4: for x being Element of X holds g . x = Class RI,x ; :: thesis: f = g

now

let x be Element of X; :: thesis: f . x = g . x
f . x = Class RI,x by A3;
hence f . x = g . x by A4; :: thesis: verum

end;

hence f = g by FUNCT_2:113; :: thesis: verum