let X, Y be set ; :: thesis: for f being Function of X,Y st ( Y = {} implies X = {} ) holds
f " Y = X
let f be Function of X,Y; :: thesis: ( ( Y = {} implies X = {} ) implies f " Y = X )
(rng f) /\ Y = rng f by XBOOLE_1:28;
then A1: f " Y = f " (rng f) by RELAT_1:133;
assume ( Y <> {} or X = {} ) ; :: thesis: f " Y = X
then dom f = X by Def1;
hence f " Y = X by A1, RELAT_1:134; :: thesis: verum