let C be Category; :: thesis: for a, b 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 a, b 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;

f is Morphism of a,b by A2, CAT_1:4;

hence f = h by A3

.= term (a,b) by A3 ;

:: thesis: verum

for f being Morphism of C st b is terminal & dom f = a & cod f = b holds

term (a,b) = f

let a, b 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;

f is Morphism of a,b by A2, CAT_1:4;

hence f = h by A3

.= term (a,b) by A3 ;

:: thesis: verum