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Metamath Proof Explorer

Theorem tvclmod

Description: A topological vector space is a left module. (Contributed by Mario Carneiro, 5-Oct-2015)

		Ref	Expression
	Assertion	tvclmod	⊢ ( 𝑊 ∈ TopVec → 𝑊 ∈ LMod )

Step	Hyp	Ref	Expression
1		tvctlm	⊢ ( 𝑊 ∈ TopVec → 𝑊 ∈ TopMod )
2		tlmlmod	⊢ ( 𝑊 ∈ TopMod → 𝑊 ∈ LMod )
3	1 2	syl	⊢ ( 𝑊 ∈ TopVec → 𝑊 ∈ LMod )