let X, Y be set ; :: thesis: for f being Function of X,Y st ( Y = {} implies X = {} ) holds
f .: X = rng f
let f be Function of X,Y; :: thesis: ( ( Y = {} implies X = {} ) implies f .: X = rng f )
assume ( Y <> {} or X = {} ) ; :: thesis: f .: X = rng f
then dom f = X by Def1;
hence f .: X = rng f by RELAT_1:146; :: thesis: verum