Metamath Proof Explorer

Theorem nmhmrcl1

Description: Reverse closure for a normed module homomorphism. (Contributed by Mario Carneiro, 18-Oct-2015)

		Ref	Expression
	Assertion	nmhmrcl1	$⊢ F \in (S NMHom T) \to S \in NrmMod$

Step	Hyp	Ref	Expression
1		isnmhm	$⊢ F \in (S NMHom T) \leftrightarrow ((S \in NrmMod \land T \in NrmMod) \land (F \in (S LMHom T) \land F \in (S NGHom T)))$
2	1	simplbi	$⊢ F \in (S NMHom T) \to (S \in NrmMod \land T \in NrmMod)$
3	2	simpld	$⊢ F \in (S NMHom T) \to S \in NrmMod$