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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 ∈ Ban → 𝑊 ∈ NrmMod )

Proof

Step Hyp Ref Expression
1 bnnvc ⊢ ( 𝑊 ∈ Ban → 𝑊 ∈ NrmVec )
2 nvcnlm ⊢ ( 𝑊 ∈ NrmVec → 𝑊 ∈ NrmMod )
3 1 2 syl ⊢ ( 𝑊 ∈ Ban → 𝑊 ∈ NrmMod )