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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 e. Ban -> W e. LMod )

Proof

Step Hyp Ref Expression
1 bnnlm 
 |-  ( W e. Ban -> W e. NrmMod )
2 nlmlmod 
 |-  ( W e. NrmMod -> W e. LMod )
3 1 2 syl 
 |-  ( W e. Ban -> W e. LMod )