let C be category; :: thesis: for o1, o2 being Object of C
for m, m9 being Morphism of o1,o2 st m is _zero & m9 is _zero & ex O being Object of C st O is _zero holds
m = m9
let o1, o2 be Object of C; :: thesis: for m, m9 being Morphism of o1,o2 st m is _zero & m9 is _zero & ex O being Object of C st O is _zero holds
m = m9
let m, m9 be Morphism of o1,o2; :: thesis: ( m is _zero & m9 is _zero & ex O being Object of C st O is _zero implies m = m9 )
assume that
A1: m is _zero and
A2: m9 is _zero ; :: thesis: ( for O being Object of C holds not O is _zero or m = m9 )
given O being Object of C such that A3: O is _zero ; :: thesis: m = m9
set n = the Morphism of O,O;
set b = the Morphism of O,o2;
set a = the Morphism of o1,O;
thus m = ( the Morphism of O,o2 * (( the Morphism of O,O ") * the Morphism of O,O)) * the Morphism of o1,O by A1, A3
.= m9 by A2, A3 ; :: thesis: verum