Metamath Proof Explorer

Theorem bnlmod

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

Ref Expression
Assertion bnlmod ⊢ W ∈ Ban → W ∈ LMod

Proof

Step Hyp Ref Expression
1 bnnlm ⊢ W ∈ Ban → W ∈ NrmMod
2 nlmlmod ⊢ W ∈ NrmMod → W ∈ LMod
3 1 2 syl ⊢ W ∈ Ban → W ∈ LMod