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Metamath Proof Explorer

Theorem lveclmod

Description: A left vector space is a left module. (Contributed by NM, 9-Dec-2013)

Ref Expression
Assertion lveclmod ⊢ W ∈ LVec → W ∈ LMod

Proof

Step Hyp Ref Expression
1 eqid ⊢ Scalar ⁡ W = Scalar ⁡ W
2 1 islvec ⊢ W ∈ LVec ↔ W ∈ LMod ∧ Scalar ⁡ W ∈ DivRing
3 2 simplbi ⊢ W ∈ LVec → W ∈ LMod