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