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 )