Theorem nmhmnghm

Description: A normed module homomorphism is a normed group homomorphism. (Contributed by Mario Carneiro, 18-Oct-2015)

	Ref	Expression
Assertion	nmhmnghm	|- ( F e. ( S NMHom T ) -> F e. ( S NGHom T ) )

Proof

Step	Hyp	Ref	Expression
1		isnmhm	|- ( F e. ( S NMHom T ) <-> ( ( S e. NrmMod /\ T e. NrmMod ) /\ ( F e. ( S LMHom T ) /\ F e. ( S NGHom T ) ) ) )
2	1	simprbi	|- ( F e. ( S NMHom T ) -> ( F e. ( S LMHom T ) /\ F e. ( S NGHom T ) ) )
3	2	simprd	|- ( F e. ( S NMHom T ) -> F e. ( S NGHom T ) )