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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 e. Ban -> W e. NrmMod )

Proof

Step Hyp Ref Expression
1 bnnvc 
 |-  ( W e. Ban -> W e. NrmVec )
2 nvcnlm 
 |-  ( W e. NrmVec -> W e. NrmMod )
3 1 2 syl 
 |-  ( W e. Ban -> W e. NrmMod )