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Metamath Proof Explorer

Theorem tlmtps

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

		Ref	Expression
	Assertion	tlmtps	⊢ ( 𝑊 ∈ TopMod → 𝑊 ∈ TopSp )

Step	Hyp	Ref	Expression
1		tlmtmd	⊢ ( 𝑊 ∈ TopMod → 𝑊 ∈ TopMnd )
2		tmdtps	⊢ ( 𝑊 ∈ TopMnd → 𝑊 ∈ TopSp )
3	1 2	syl	⊢ ( 𝑊 ∈ TopMod → 𝑊 ∈ TopSp )