let C be non empty non void CatStr ; :: thesis: for a, b being Object of C
for f being Morphism of a,b st Hom a,b <> {} holds
( dom f = a & cod f = b )
let a, b be Object of C; :: thesis: for f being Morphism of a,b st Hom a,b <> {} holds
( dom f = a & cod f = b )
let f be Morphism of a,b; :: thesis: ( Hom a,b <> {} implies ( dom f = a & cod f = b ) )
assume Hom a,b <> {} ; :: thesis: ( dom f = a & cod f = b )
then f in Hom a,b by Def7;
hence ( dom f = a & cod f = b ) by Th18; :: thesis: verum