let X, Y be set ; :: thesis: for f being Function of X,Y st ( Y = {} implies X = {} ) holds
f in Funcs X,Y
let f be Function of X,Y; :: thesis: ( ( Y = {} implies X = {} ) implies f in Funcs X,Y )
assume ( Y = {} implies X = {} ) ; :: thesis: f in Funcs X,Y
then A1: dom f = X by Def1;
rng f c= Y ;
hence f in Funcs X,Y by A1, Def2; :: thesis: verum