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 :: thesis: for x being Element of X holds f . x = g . x

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_2:63; :: thesis: verum