Description: A normed group homomorphism is a group homomorphism. (Contributed by Mario Carneiro, 18-Oct-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | nghmghm | |- ( F e. ( S NGHom T ) -> F e. ( S GrpHom T ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid | |- ( S normOp T ) = ( S normOp T ) |
|
2 | 1 | isnghm | |- ( F e. ( S NGHom T ) <-> ( ( S e. NrmGrp /\ T e. NrmGrp ) /\ ( F e. ( S GrpHom T ) /\ ( ( S normOp T ) ` F ) e. RR ) ) ) |
3 | 2 | simprbi | |- ( F e. ( S NGHom T ) -> ( F e. ( S GrpHom T ) /\ ( ( S normOp T ) ` F ) e. RR ) ) |
4 | 3 | simpld | |- ( F e. ( S NGHom T ) -> F e. ( S GrpHom T ) ) |