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
( dom f = the_carrier_of a & rng f c= the_carrier_of b )
let a, b be Object of C; :: thesis: ( <^a,b^> <> {} implies for f being Morphism of a,b holds
( dom f = the_carrier_of a & rng f c= the_carrier_of b ) )
assume A1: <^a,b^> <> {} ; :: thesis: for f being Morphism of a,b holds
( dom f = the_carrier_of a & rng f c= the_carrier_of b )
let f be Morphism of a,b; :: thesis: ( dom f = the_carrier_of a & rng f c= 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 ( dom f = the_carrier_of a & rng f c= the_carrier_of b ) by A2, FUNCT_2:92; :: thesis: verum