let C be Category; :: thesis: for b, a being Object of C
for f being Morphism of C st b is terminal & dom f = a & cod f = b holds
term a,b = f
let b, a be Object of C; :: thesis: for f being Morphism of C st b is terminal & dom f = a & cod f = b holds
term a,b = f
let f be Morphism of C; :: thesis: ( b is terminal & dom f = a & cod f = b implies term a,b = f )
assume that
A1: b is terminal and
A2: ( dom f = a & cod f = b ) ; :: thesis: term a,b = f
consider h being Morphism of a,b such that
A3: for g being Morphism of a,b holds h = g by A1, CAT_1:def 15;
f is Morphism of a,b by A2, CAT_1:22;
hence f = h by A3
.= term a,b by A3 ;
:: thesis: verum