let C, D, E be non empty set ; :: thesis: for f being Function of [:C,D:],E holds curry f is Function of C,(Funcs D,E)
let f be Function of [:C,D:],E; :: thesis: curry f is Function of C,(Funcs D,E)
A1: dom f = [:C,D:] by FUNCT_2:def 1;
then A2: dom (curry f) = C by FUNCT_5:31;
rng (curry f) c= Funcs D,E

proof

let x be set ; :: according to TARSKI:def 3 :: thesis: ( not x in rng (curry f) or x in Funcs D,E )
assume A3: x in rng (curry f) ; :: thesis: x in Funcs D,E
rng (curry f) c= Funcs D,(rng f) by A1, FUNCT_5:42;
then consider g being Function such that
A4: x = g and
A5: dom g = D and
A6: rng g c= rng f by A3, FUNCT_2:def 2;
rng f c= E by RELAT_1:def 19;
then rng g c= E by A6, XBOOLE_1:1;
then ( g is Function of D,E & E <> {} ) by A5, FUNCT_2:def 1, RELSET_1:11;
hence x in Funcs D,E by A4, FUNCT_2:11; :: thesis: verum

end;

hence curry f is Function of C,(Funcs D,E) by A2, FUNCT_2:def 1, RELSET_1:11; :: thesis: verum