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)
A2: <^a,b^> c= Funcs ((the_carrier_of a),(the_carrier_of b)) by Th33;
f in <^a,b^> by A1;
hence f is Function of (the_carrier_of a),(the_carrier_of b) by A2, FUNCT_2:66; :: thesis: verum