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Metamath Proof Explorer

Theorem bnnlm

Description: A Banach space is a normed module. (Contributed by Mario Carneiro, 15-Oct-2015)

		Ref	Expression
	Assertion	bnnlm	$⊢ W \in Ban \to W \in NrmMod$

Step	Hyp	Ref	Expression
1		bnnvc	$⊢ W \in Ban \to W \in NrmVec$
2		nvcnlm	$⊢ W \in NrmVec \to W \in NrmMod$
3	1 2	syl	$⊢ W \in Ban \to W \in NrmMod$