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Metamath Proof Explorer

Theorem mstps

Description: A metric space is a topological space. (Contributed by Mario Carneiro, 26-Aug-2015)

Ref Expression
Assertion mstps ( 𝑀 ∈ MetSp → 𝑀 ∈ TopSp )

Proof

Step Hyp Ref Expression
1 msxms ⊢ ( 𝑀 ∈ MetSp → 𝑀 ∈ ∞MetSp )
2 xmstps ⊢ ( 𝑀 ∈ ∞MetSp → 𝑀 ∈ TopSp )
3 1 2 syl ⊢ ( 𝑀 ∈ MetSp → 𝑀 ∈ TopSp )