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 ( dom f = X & rng f c= Y ) by Def1;
hence f in Funcs X,Y by Def2; :: thesis: verum