Theorem bnlmod

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

	Ref	Expression
Assertion	bnlmod	$$⊢W\in \mathrm{Ban}\to W\in \mathrm{LMod}$$

Proof

Step	Hyp	Ref	Expression
1		bnnlm	$$⊢W\in \mathrm{Ban}\to W\in \mathrm{NrmMod}$$
2		nlmlmod	$$⊢W\in \mathrm{NrmMod}\to W\in \mathrm{LMod}$$
3	1 2	syl	$$⊢W\in \mathrm{Ban}\to W\in \mathrm{LMod}$$