let C be Category; :: thesis: for a, b being Object of C
for f being Morphism of C st a is initial & dom f = a & cod f = b holds
init a,b = f
let a, b be Object of C; :: thesis: for f being Morphism of C st a is initial & dom f = a & cod f = b holds
init a,b = f
let f be Morphism of C; :: thesis: ( a is initial & dom f = a & cod f = b implies init a,b = f )
assume that
A1: a is initial and
A2: ( dom f = a & cod f = b ) ; :: thesis: init 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 16;
f is Morphism of a,b by A2, CAT_1:22;
hence f = h by A3
.= init a,b by A3 ;
:: thesis: verum