let C be para-functional category; :: thesis: for a, b being object of st <^a,b^> <> {} holds
for f being Morphism of , holds f is Function of the_carrier_of a, the_carrier_of b
let a, b be object of ; :: thesis: ( <^a,b^> <> {} implies for f being Morphism of , holds f is Function of the_carrier_of a, the_carrier_of b )
assume A1: <^a,b^> <> {} ; :: thesis: for f being Morphism of , holds f is Function of the_carrier_of a, the_carrier_of b
let f be Morphism of ,; :: thesis: f is Function of the_carrier_of a, the_carrier_of b
A2: <^a,b^> c= Funcs (the_carrier_of a),(the_carrier_of b) by Th34;
f in <^a,b^> by A1;
hence f is Function of the_carrier_of a, the_carrier_of b by A2, FUNCT_2:121; :: thesis: verum