let C be para-functional category; :: thesis: for a, b being object of C st <^a,b^> <> {} holds
for f being Morphism of a,b holds f is Function of the_carrier_of a, the_carrier_of b
let a, b be object of C; :: thesis: ( <^a,b^> <> {} implies for f being Morphism of a,b holds f is Function of the_carrier_of a, the_carrier_of b )
assume A1: <^a,b^> <> {} ; :: thesis: for f being Morphism of a,b holds f is Function of the_carrier_of a, the_carrier_of b
let f be Morphism of a,b; :: thesis: f is Function of the_carrier_of a, the_carrier_of b
( <^a,b^> c= Funcs (the_carrier_of a),(the_carrier_of b) & f in <^a,b^> ) by A1, Th34;
hence f is Function of the_carrier_of a, the_carrier_of b by FUNCT_2:121; :: thesis: verum