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 )
assume ( Y <> {} or X = {} ) ; :: thesis: f " Y = X
then ( dom f = X & (rng f) /\ Y = rng f ) by Def1, XBOOLE_1:28;
then ( dom f = X & f " Y = f " (rng f) ) by RELAT_1:168;
hence f " Y = X by RELAT_1:169; :: thesis: verum