let P, X, Y be set ; :: thesis: for f being Function of X,Y st ( Y = {} implies X = {} ) & P c= X holds
P c= f " (f .: P)
let f be Function of X,Y; :: thesis: ( ( Y = {} implies X = {} ) & P c= X implies P c= f " (f .: P) )
assume ( Y <> {} or X = {} ) ; :: thesis: ( not P c= X or P c= f " (f .: P) )
then dom f = X by Def1;
hence ( not P c= X or P c= f " (f .: P) ) by FUNCT_1:76; :: thesis: verum